{"id":4984,"date":"2022-10-13T18:12:39","date_gmt":"2022-10-13T18:12:39","guid":{"rendered":"https:\/\/www.studyzonebd.com\/math\/?p=4984"},"modified":"2022-10-13T18:13:53","modified_gmt":"2022-10-13T18:13:53","slug":"class-8-chapter-4-lesson-4-2","status":"publish","type":"post","link":"https:\/\/www.studyzonebd.com\/math\/class-8-chapter-4-lesson-4-2\/","title":{"rendered":"\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e8 | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf"},"content":{"rendered":"\n

\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math <\/a>Book Solution | Chapter <\/a>04 : Algebraic formulas and applications| Class 8 math book Online Solution in Bangla (BD)<\/p>\n\n\n\n

\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997| \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e8: \u0998\u09a8\u09ab\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u0985\u09a8\u09c1\u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4 – PDF<\/a><\/h4>\n\n\n\n

\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e8 \u098f\u09b0 \u09b8\u0995\u09b2 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u0989\u09a4\u09cd\u09a4\u09b0 \u098f\u0996\u09be\u09a8\u09c7 \u09b0\u09df\u09c7\u099b\u09c7\u0964 \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/p>\n\n\n\n

\u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf\u09b0 \u0997\u09a3\u09bf\u09a4 \u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e8 \u09aa\u09cd\u09b0\u09b6\u09cd\u09a8 \u0993 \u09b8\u09ae\u09be\u09a7\u09be\u09a8<\/strong><\/span><\/h4>\n\n\n\n

\u09e7\u0964 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u09b0\u09be\u09b6\u09bf\u0997\u09c1\u09b2\u09cb\u09b0 \u0998\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

(\u0995) 3x + y    (\u0996) x2<\/sup> + y     (\u0997) 5 p + 2q     (\u0998) a2<\/sup>b + c2<\/sup>d       (\u0999) 6 p – 7<\/p>\n\n\n\n

(\u099a) ax \u2013 by     (\u099b) 2 p2<\/sup> – 3r 2<\/sup> (\u099c) x3<\/sup> + 2     (\u099d) 2m + 3n – 5 p<\/p>\n\n\n\n

(\u099e) x2<\/sup> – y 2<\/sup> + z 2<\/sup>     (\u099f) a2<\/sup>b2 <\/sup>– c2<\/sup>d 2<\/sup>        (\u09a0) a2<\/sup>b – b3<\/sup>c     (\u09a1) x3<\/sup> – 2 y3<\/sup><\/p>\n\n\n\n

(\u09a2) 11a -12b              (\u09a3) x3<\/sup> + y3<\/sup><\/a><\/p>\n\n\n\n

(\u0995) 3x + y<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(3x + y)3<\/sup>=(3x)3<\/sup> +3* (3x)2<\/sup> * y + 3* (3x) * ( y)2<\/sup> + (y)3<\/sup><\/p>\n\n\n\n

                        =27x3<\/sup> +3* 9x2<\/sup> * y + 3* (3x) * ( y)2<\/sup> + (y)3<\/sup><\/p>\n\n\n\n

                        =27x3<\/sup> +27x2<\/sup> y + 9x y2<\/sup> + y3<\/sup><\/p>\n\n\n\n

(\u0996) x2<\/sup> + y<\/strong>  <\/strong>     <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x2<\/sup> + y)3<\/sup>=(x2<\/sup>)3<\/sup>+3*(x2<\/sup>)2 <\/sup>*y+3* x2<\/sup>*y2<\/sup>+y3<\/sup><\/p>\n\n\n\n

                <\/sup>=x6<\/sup>+3*x4<\/sup>*y+3*x2<\/sup>*y2<\/sup>+y3<\/sup><\/p>\n\n\n\n

                = x6<\/sup>+3x4<\/sup>y+3x2<\/sup>y2<\/sup>+y3<\/sup><\/p>\n\n\n\n

(\u0997) 5 p + 2q <\/strong> <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(5 p + 2q)3<\/sup>=(5 p)3<\/sup> + 3* (5 p)2<\/sup> * 2q + 3* (5 p) * (2q)2<\/sup> + (2q)3<\/sup><\/p>\n\n\n\n

= 125 p3<\/sup> + 3* 25 p2<\/sup> * 2q + 3* 5 p * 4q2<\/sup> + 8q3<\/sup><\/p>\n\n\n\n

=125 p3<\/sup> +150 p2<\/sup>q + 60 pq 2<\/sup> + 8q3<\/sup><\/p>\n\n\n\n

(\u0998) a2<\/sup>b + c2<\/sup>d<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(a2<\/sup>b + c2<\/sup>d)3<\/sup>= (a2<\/sup>b)3<\/sup> + 3* (a 2<\/sup>b)2<\/sup> * c2<\/sup> d + 3* (a2<\/sup> b) * (c2<\/sup> d)2<\/sup> + (c2<\/sup> d)3<\/sup><\/p>\n\n\n\n

= a6<\/sup>b3<\/sup> + 3* a4<\/sup>b2<\/sup> * c2<\/sup>d + 3* a2<\/sup>b * c4<\/sup>d 2<\/sup> + c6<\/sup>d 3<\/sup><\/p>\n\n\n\n

=a6<\/sup>b3<\/sup> + 3a4<\/sup>b2<\/sup>c2<\/sup>d + 3a2<\/sup>bc4<\/sup>d 2<\/sup> + c6<\/sup>d 3<\/sup><\/p>\n\n\n\n

(\u0999) 6 p \u2013 7<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(6 p \u2013 7)3<\/sup>=(6p)3<\/sup>-3*(6p)2<\/sup>*7+3*(6p)*(7)2<\/sup>-(7)3<\/sup><\/p>\n\n\n\n

            =216p3<\/sup>-3*36p2<\/sup>*7+3*(6p)*49-343<\/p>\n\n\n\n

            =216p3<\/sup>-756p2<\/sup>+882p-343<\/p>\n\n\n\n

(\u099a) ax \u2013 by<\/strong> <\/strong>    <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(ax \u2013 by)3<\/sup>=(ax)3<\/sup>-3*(ax)2<\/sup>*by+3*(ax)*(by)2<\/sup>-(by)3<\/sup><\/p>\n\n\n\n

                                <\/sup>=a3<\/sup>x3<\/sup>-3*a2<\/sup>x2<\/sup>*by+3*ax*b2<\/sup>y2<\/sup>-b3<\/sup>y3<\/sup><\/p>\n\n\n\n

                                <\/sup>= a3<\/sup>x3<\/sup>-3a2<\/sup>x2<\/sup>by+3axb2<\/sup>y2<\/sup>-b3<\/sup>y3<\/sup><\/p>\n\n\n\n

(\u099b) 2 p2<\/sup> – 3r 2<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(2p2<\/sup> – 3r 2<\/sup>)3<\/sup>=(2p2<\/sup>)3<\/sup>-3*(2p2<\/sup>)2<\/sup>*3r2<\/sup>+3*(2p2<\/sup>)*(3r2<\/sup>)2<\/sup>-(3r2<\/sup>)3<\/sup><\/p>\n\n\n\n

                        =8p6<\/sup>-3*4p4<\/sup>*3r2<\/sup>+3*2p2<\/sup>*9r4<\/sup>-27r6<\/sup><\/p>\n\n\n\n

                         <\/sup>=8p6<\/sup>-36p4<\/sup>r2<\/sup>+54p2<\/sup>r4<\/sup>-27r6<\/sup><\/p>\n\n\n\n

(\u099c) x3<\/sup> + 2 <\/strong> <\/strong>    <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x3<\/sup> + 2)3<\/sup>=(x3<\/sup>)3<\/sup>+3*(x3<\/sup>)2<\/sup>*2+3*(x3<\/sup>)*(2)2<\/sup>+(2)3<\/sup><\/p>\n\n\n\n

                <\/sup>=x9<\/sup>+3*x6<\/sup>*2+3*x3<\/sup>*4+8<\/sup><\/p>\n\n\n\n

        =x9<\/sup>+6x6<\/sup>+12x3<\/sup>+8<\/p>\n\n\n\n

(\u099d) 2m + 3n – 5 p<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(2m + 3n – 5 p)3<\/sup>={(2m +3n) – (5 p)}3<\/sup><\/p>\n\n\n\n

= (2m+ 3n)3<\/sup> \u2013 3*(2m+ 3n)2<\/sup> * (5 p) + 3*(2m+ 3n)*(5p)2<\/sup> \u2013 (5 p)3<\/sup><\/p>\n\n\n\n

= {(2m)3<\/sup> + 3* (2m)2<\/sup> * 3n + 3* (2m) * (3n)2<\/sup> + (3n)3<\/sup>} -15 p *{(2m)2<\/sup> + 2* 2m*3n + (3n)2<\/sup>}+ 3* (2m + 3n)* 25 p2<\/sup> -125 p3<\/sup><\/p>\n\n\n\n

= 8m3<\/sup> +  4m2<\/sup> * 9n + 6m* 9n2<\/sup> + 27n3<\/sup> -15 p *{4m2<\/sup> +2* 2m*3n + (3n)2<\/sup>}+ 3* (2m + 3n)* 25 p2<\/sup> -125 p3<\/sup><\/p>\n\n\n\n

=8m3<\/sup> +  36m2<\/sup> n + 36mn2<\/sup> + 27n3<\/sup> -15 p *4m2<\/sup> -15p*2* 2m*3n -15p* 9n2<\/sup>+ 6m*25p2<\/sup> + 9n* 25p2<\/sup> -125 p3<\/sup><\/p>\n\n\n\n

=8m3<\/sup> +  36m2<\/sup> n + 36mn2<\/sup> + 27n3<\/sup> -60 pm2<\/sup> -180pmn -135pn2<\/sup>+ 150mp2<\/sup> + 225np2<\/sup> -125 p3<\/sup><\/p>\n\n\n\n

(\u099e) x2<\/sup> – y 2<\/sup> + z 2<\/sup> <\/strong>       <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x2<\/sup> – y 2<\/sup> + z 2<\/sup>)3<\/sup><\/p>\n\n\n\n

={( x2<\/sup> – y 2<\/sup>) + (z 2<\/sup>)}3<\/sup><\/p>\n\n\n\n

= (x2<\/sup> – y2<\/sup> )3<\/sup> + 3(x2<\/sup> – y2<\/sup> )2 z2<\/sup> + 3(x2<\/sup> – y2<\/sup> )(z2<\/sup> )2<\/sup> + (z2<\/sup> )3<\/sup><\/p>\n\n\n\n

= {(x2<\/sup> )3<\/sup> – 3(x2<\/sup> )2<\/sup> y2<\/sup> + 3x2 <\/sup>( y2<\/sup> )2<\/sup> – ( y2<\/sup> )3<\/sup>} +3(x2<\/sup> – y2<\/sup> )2<\/sup> z2<\/sup> + 3(x2<\/sup> – y2<\/sup> )(z2<\/sup> )2<\/sup> + (z2<\/sup> )3<\/sup><\/p>\n\n\n\n

= x6<\/sup> – 3x4<\/sup> y2<\/sup> + 3x2<\/sup> y4<\/sup> – y6<\/sup> + 3z2<\/sup>{(x2<\/sup> )2<\/sup> + 2x2<\/sup> y2<\/sup> + ( y2<\/sup> )2<\/sup>}+ 3z4<\/sup> (x2<\/sup> – y2<\/sup> ) + z6<\/sup><\/p>\n\n\n\n

= x6<\/sup> – 3x4<\/sup> y2<\/sup> + 3x2<\/sup> y4<\/sup> – y6 + 3x4<\/sup> z2<\/sup> – 6x2<\/sup> y2<\/sup> z2<\/sup> + 3y6<\/sup> z2<\/sup> + 3z4<\/sup> x2<\/sup> – 3z4<\/sup> y2<\/sup> + z6<\/sup><\/p>\n\n\n\n

= x6<\/sup> – y6<\/sup> + z6<\/sup> – 3x4<\/sup> y2<\/sup> + 3x2<\/sup> y4<\/sup> + 3x4<\/sup> z2<\/sup> – 6x2<\/sup> y2<\/sup> z2 <\/sup>+ 3y6<\/sup> z2<\/sup> +3x2<\/sup> z4<\/sup> – 3y2<\/sup> z4<\/sup><\/p>\n\n\n\n

(\u099f) a2<\/sup>b2 <\/sup>– c2<\/sup>d 2<\/sup><\/strong>            <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(a2<\/sup>b2<\/sup> – c2<\/sup>d 2<\/sup> )3<\/sup> = (a2<\/sup>b2<\/sup>) 3<\/sup> \u2013 3* (a2<\/sup>b2<\/sup> )2<\/sup> * c 2<\/sup>d2<\/sup> + 3* (a2<\/sup> b2<\/sup> )* (c2<\/sup> d2<\/sup> )2<\/sup> \u2013 (c2<\/sup> d2<\/sup>)3<\/sup><\/p>\n\n\n\n

= a6<\/sup>b6<\/sup> – 3a4<\/sup>b4<\/sup>c2<\/sup>d 2<\/sup> + 3a2<\/sup>b2<\/sup>c4<\/sup>d 4<\/sup> – c6<\/sup>d 6<\/sup><\/p>\n\n\n\n

(\u09a0) a2<\/sup>b – b3<\/sup>c<\/strong>   <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(a2<\/sup>b – b3<\/sup>c)3<\/sup>= (a2<\/sup>b) 3<\/sup> \u2013 3* (a2<\/sup> b2<\/sup>)2<\/sup> * b3<\/sup> c + 3 (a2<\/sup> b)* (b3<\/sup> c)2<\/sup> \u2013 (b3<\/sup> c)3<\/sup><\/p>\n\n\n\n

=a6<\/sup>b3<\/sup> – 3a4<\/sup>b2<\/sup>b3<\/sup>c + 3a2<\/sup>bb6<\/sup>c2 <\/sup>– b9<\/sup>c3<\/sup><\/p>\n\n\n\n

=a6<\/sup>b3<\/sup> – 3a4<\/sup>b5<\/sup>c + 3a2<\/sup>b7<\/sup>c2<\/sup> – b9<\/sup>c3<\/sup><\/p>\n\n\n\n

(\u09a1) x3<\/sup> – 2 y<\/strong>3<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x3<\/sup> -2y3<\/sup> )3<\/sup> =( x3<\/sup>) 3<\/sup> \u2013 3* (x3<\/sup> )2<\/sup> * 2y3<\/sup> + 3* (x3<\/sup> )* (2 y3<\/sup> )2<\/sup> + (2y3<\/sup>)3<\/sup><\/p>\n\n\n\n

= x9 – 6x6<\/sup> y3 + 12 x3<\/sup> y6<\/sup> – 8y9<\/sup><\/p>\n\n\n\n

(\u09a2) 11a -12b<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(11a -12b)3<\/sup> = (11a)3<\/sup> \u2013 3* (11a)2<\/sup> *12b + 3* (11a)* (12b)2<\/sup> \u2013 (12b)3<\/sup><\/p>\n\n\n\n

=1331a3<\/sup> – 4356a2<\/sup>b+ 4752ab2<\/sup> -1728b3<\/sup><\/p>\n\n\n\n

(\u09a3) x3<\/sup> + y3<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x3<\/sup> + y3<\/sup> )3<\/sup> =( x3<\/sup>) 3<\/sup> + 3* (x3<\/sup> )2<\/sup> * y3<\/sup> + 3* (x3<\/sup> )* ( y3<\/sup> )2<\/sup> +( y3<\/sup>)3<\/sup><\/p>\n\n\n\n

= x9<\/sup> + 3x6<\/sup> y3 <\/sup>+ 3x3<\/sup> y6<\/sup> + y9<\/sup><\/p>\n\n\n\n

\u09e8\u0964 \u09b8\u09b0\u09b2 \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

(\u0995) (3x + y)3 <\/sup>+ 3(3x + y)2<\/sup> (3x – y) + 3(3x + y)(3x – y)2<\/sup> + (3x – y)3<\/sup><\/p>\n\n\n\n

(\u0996) (2 p + 5q)3<\/sup> + 3(2 p + 5q)2<\/sup> (5q – 2 p) + 3(2 p + 5q)(5q – 2 p)2<\/sup> + (5q – 2 p)3<\/sup><\/p>\n\n\n\n

(\u0997) ( x + 2 y)3 <\/sup>– 3( x + 2 y)2<\/sup> (x – 2 y) + 3( x + 2 y)( x – 2 y)2<\/sup> – (x – 2 y)3<\/sup><\/p>\n\n\n\n

(\u0998) (6m + 2)3<\/sup> – 3(6m + 2)2<\/sup> (6m – 4) + 3(6m + 2)(6m – 4)2<\/sup> + (6m – 4)3<\/sup><\/p>\n\n\n\n

(\u0999) ( x – y)3<\/sup> + ( x + y)3<\/sup> + 6x(x2<\/sup> – y2<\/sup>)<\/p>\n\n\n\n

(\u0995) (3x + y)3 <\/sup>+ 3(3x + y)2<\/sup> (3x – y) + 3(3x + y)(3x – y)2<\/sup> + (3x – y)<\/strong>3<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a7\u09b0\u09bf, 3x + y = a<\/p>\n\n\n\n

\u098f\u09ac\u0982 3x – y = b<\/p>\n\n\n\n

\u2234 (3x + y)3 <\/sup>+ 3(3x + y)2<\/sup> (3x – y) + 3(3x + y)(3x – y)2<\/sup> + (3x – y)3<\/sup><\/p>\n\n\n\n

=a3<\/sup> + 3a2<\/sup>b + 3ab2<\/sup> + b3<\/sup><\/p>\n\n\n\n

= (a + b)3<\/sup><\/p>\n\n\n\n

= (3x + y + 3x – y)3 <\/sup>[\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

= (6x)3<\/sup><\/p>\n\n\n\n

= 216x3<\/sup><\/p>\n\n\n\n

(\u0996) (2 p + 5q)3<\/sup> + 3(2 p + 5q)2<\/sup> (5q – 2 p) + 3(2 p + 5q)(5q – 2 p)2<\/sup> + (5q – 2 p)3<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a7\u09b0\u09bf, 2p+5q=a<\/p>\n\n\n\n

\u098f\u09ac\u0982,5q-2p=b<\/p>\n\n\n\n

\u2234 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a3<\/sup> + 3a2<\/sup>b + 3ab2<\/sup> + b3<\/sup><\/p>\n\n\n\n

                        =(a+b)3<\/sup><\/p>\n\n\n\n

                        =(2p+5q+5q-2p)3<\/sup>  [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

                        =(10q)3             <\/sup><\/p>\n\n\n\n

                         <\/sup>=1000q3<\/sup><\/p>\n\n\n\n

(\u0997) ( x + 2 y)3 <\/sup>– 3( x + 2 y)2<\/sup> (x – 2 y) + 3( x + 2 y)( x – 2 y)2<\/sup> – (x – 2 y)3<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a7\u09b0\u09bf, x+2y=a<\/p>\n\n\n\n

\u098f\u09ac\u0982, x-2y=b<\/p>\n\n\n\n

\u2234 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a3<\/sup> – 3a2<\/sup>b + 3ab2<\/sup> – b3<\/sup><\/p>\n\n\n\n

                        =(a-b)3<\/sup><\/p>\n\n\n\n

                        ={(x+27)-(x-2y)}3<\/sup> [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

                        =(x+2y-x+2y)3<\/sup><\/p>\n\n\n\n

                        =(4y)3<\/sup><\/p>\n\n\n\n

                         <\/sup>=64y3<\/sup><\/p>\n\n\n\n

(\u0998) (6m + 2)3<\/sup> – 3(6m + 2)2<\/sup> (6m – 4) + 3(6m + 2)(6m – 4)2<\/sup> + (6m – 4)<\/strong>3<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a7\u09b0\u09bf, 6m+2=a<\/p>\n\n\n\n

\u098f\u09ac\u0982 6m-4=b<\/p>\n\n\n\n

\u2234 \u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a3<\/sup> – 3a2<\/sup>b + 3ab2<\/sup> – b3<\/sup><\/p>\n\n\n\n

                        =(a-b)3<\/sup><\/p>\n\n\n\n

                        ={(6m+2)-(6m-4)}3<\/sup>   [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

                        =(6m+2-6m+4)3<\/sup><\/p>\n\n\n\n

                        =63<\/sup><\/p>\n\n\n\n

                        =216<\/p>\n\n\n\n

(\u0999) ( x – y)3<\/sup> + ( x + y)3<\/sup> + 6x(x2<\/sup> – y2<\/sup>)<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a7\u09b0\u09bf, x-y=a<\/p>\n\n\n\n

\u098f\u09ac\u0982, x+y=b<\/p>\n\n\n\n

\u2234a+b=x-y+x-y=2x<\/p>\n\n\n\n

\u098f\u0996\u09a8, ( x – y)3<\/sup> + ( x + y)3<\/sup> + 6x(x2<\/sup> – y2<\/sup>)<\/p>\n\n\n\n

=(x – y)3<\/sup> + ( x + y)3<\/sup> + 3*2x*(x – y)(x+y)        [x2<\/sup>-y2<\/sup>=(x+y)(x-y)]<\/p>\n\n\n\n

=a3<\/sup>+b3<\/sup>+3*(a+b)*a*b [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

=a3<\/sup>+b3<\/sup>+3ab(a+b)<\/p>\n\n\n\n

=(a+b)3<\/sup><\/p>\n\n\n\n

=(2x)3<\/sup>  [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

=8x3<\/sup><\/p>\n\n\n\n

\u09e9\u0964 a+b=8 \u098f\u09ac\u0982 ab=15 \u09b9\u09b2\u09c7  a3<\/sup>+b3<\/sup> \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a+b=8 \u098f\u09ac\u0982 ab=15<\/p>\n\n\n\n

\u2234\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a3<\/sup>+b3    <\/sup>           <\/p>\n\n\n\n

                        =(a+b)3<\/sup>-3ab(a+b)<\/p>\n\n\n\n

                        =83<\/sup>-3*15*8<\/p>\n\n\n\n

                        =512-360                 <\/p>\n\n\n\n

                        =152<\/p>\n\n\n\n

\u09ea\u0964 x+y=2 \u09b9\u09b2\u09c7, \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, x3<\/sup>+y3<\/sup>+6xy=8<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x+y=2<\/p>\n\n\n\n

\u09a6\u09c7\u0996\u09be\u09a4\u09c7 \u09b9\u09ac\u09c7, x3<\/sup>+y3<\/sup>+6xy=8<\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7= x3<\/sup>+y3<\/sup>+6xy<\/p>\n\n\n\n

            = x3<\/sup>+y3<\/sup>+3xy.2<\/p>\n\n\n\n

            = x3<\/sup>+y3<\/sup>+3xy(x+y)   [x+y=2]<\/p>\n\n\n\n

            =(x+y)3<\/sup><\/p>\n\n\n\n

            =23<\/sup>      [\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

            =8      <\/p>\n\n\n\n

   =\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09b2\u09cb)<\/p>\n\n\n\n

\u09eb\u0964 2x+3y=13 \u098f\u09ac\u0982 xy=6 \u09b9\u09b2\u09c7,  8x3<\/sup>+27y3 <\/sup>\u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, 2x+3y=13 \u098f\u09ac\u0982 xy=6<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf=8x3<\/sup>+27y3<\/sup><\/p>\n\n\n\n

            =(2x)3<\/sup>+(3y)3   <\/sup><\/p>\n\n\n\n

            =(2x+3y)3<\/sup>-3*2x*3y*(2x+3y)<\/p>\n\n\n\n

            =(13)3<\/sup>-18xy(13)<\/p>\n\n\n\n

            =(13)3<\/sup>-18*6*13<\/p>\n\n\n\n

            =2197-1404<\/p>\n\n\n\n

            =793<\/p>\n\n\n\n

\u09ec\u0964 p-q=5 \u098f\u09ac\u0982 pq=3 \u09b9\u09b2\u09c7, p3<\/sup>-q3<\/sup> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0\u0964<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, p-q=5 \u098f\u09ac\u0982 pq=3<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= p3<\/sup>-q3<\/sup><\/p>\n\n\n\n

                        =(p-q)3<\/sup>+3pq(p-q)<\/p>\n\n\n\n

                        =53<\/sup>+3*3*5<\/p>\n\n\n\n

                        =125+45      <\/p>\n\n\n\n

                        =170  <\/p>\n\n\n\n

\u09ed\u0964 x-2y=3 \u09b9\u09b2\u09c7, x3<\/sup>-8y3<\/sup>-18xy \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0?<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x-2y=3<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= x3<\/sup>-8y3<\/sup>-18xy<\/p>\n\n\n\n

                        = x3<\/sup>-(2y)3<\/sup>-3.x.2y.3<\/p>\n\n\n\n

                        = x3<\/sup>-(2y)3<\/sup>-3.x.2y.(x-2y)     [x-2y=3)<\/p>\n\n\n\n

                        =(x-2y)3<\/sup><\/p>\n\n\n\n

                        <\/sup>=33   <\/sup>[\u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7]<\/p>\n\n\n\n

                        =27<\/p>\n\n\n\n

\u09ee\u0964 4x-3=5 \u09b9\u09b2\u09c7, \u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0 \u09af\u09c7, 64x3<\/sup>-27-180x=125<\/strong><\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7,  4x-3=5<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, 64x3<\/sup>-27-180x=125<\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7=64x3<\/sup>-27-180x<\/p>\n\n\n\n

            =(4x)3<\/sup>-33<\/sup>-180x<\/p>\n\n\n\n

            =(4x-3)3<\/sup>+3.4x.3(4x-3)-180x<\/p>\n\n\n\n

            =53<\/sup>+36.x.5-180x<\/p>\n\n\n\n

            =53<\/sup>+180x-180x<\/p>\n\n\n\n

            =53<\/sup><\/p>\n\n\n\n

            =125<\/p>\n\n\n\n

   =\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 [\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4]<\/p>\n\n\n\n

\u09ef\u0964 a=-3 \u098f\u09ac\u0982 b=2 \u09b9\u09b2\u09c7, 8a3<\/sup>+36a2<\/sup>b+54ab2<\/sup>+27b3<\/sup> \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a=-3 \u098f\u09ac\u0982 b=2<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf=8a3<\/sup>+36a2<\/sup>b+54ab2<\/sup>+27b3<\/sup><\/p>\n\n\n\n

                <\/sup>=(2a)3<\/sup>+3.(2a)2 <\/sup>.3b+3.2a.(3b)2<\/sup>+(3b)3<\/sup><\/p>\n\n\n\n

            =(2a+3b)3<\/sup><\/p>\n\n\n\n

            ={2(-3)+3(2)}3<\/sup><\/p>\n\n\n\n

                <\/sup>=(-6+6)3<\/sup><\/p>\n\n\n\n

            =(0)3<\/sup><\/p>\n\n\n\n

                <\/sup>=0<\/p>\n\n\n\n

\u09a8\u09bf\u09b0\u09cd\u09a8\u09c7\u09af\u09bc \u09ae\u09be\u09a8  0<\/p>\n\n\n\n

\u09e7\u09e6\u0964 a=7 \u09b9\u09b2\u09c7, a3<\/sup>+6a2<\/sup>+12a+1 \u098f\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995\u09b0<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a=7<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a3<\/sup>+6a2<\/sup>+12a+1<\/p>\n\n\n\n

            = a3<\/sup>+3.a2<\/sup>.2+3.a.22<\/sup>+22<\/sup>-7<\/p>\n\n\n\n

            =(a+2)3<\/sup>-7<\/p>\n\n\n\n

            =(7+2)3<\/sup>-7<\/p>\n\n\n\n

            =729-7<\/p>\n\n\n\n

            =722<\/p>\n\n\n\n

\u09a8\u09bf\u09b0\u09cd\u09a8\u09c7\u09af\u09bc \u09ae\u09be\u09a8 722<\/p>\n\n\n\n

\u09e7\u09e7\u0964 x=5 \u09b9\u09b2\u09c7, x3<\/sup>-12x2<\/sup>+48x-64 \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x=5<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= x3<\/sup>-12x2<\/sup>+48x-64<\/p>\n\n\n\n

            = x3<\/sup>-3.x2<\/sup>.4+3.x.42<\/sup>-43<\/sup><\/p>\n\n\n\n

            =(x-4)3<\/sup><\/p>\n\n\n\n

                <\/sup>=(5-4)3<\/sup><\/p>\n\n\n\n

                <\/sup>=13<\/sup><\/p>\n\n\n\n

                <\/sup>=1<\/p>\n\n\n\n

\u09a8\u09bf\u09b0\u09cd\u09a8\u09c7\u09af\u09bc \u09ae\u09be\u09a8 1<\/p>\n\n\n\n

\u09e7\u09e8\u0964 a2<\/sup>+b2<\/sup>=c2  <\/sup>\u09b9\u09b2\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0 \u09af\u09c7, a6<\/sup>+b6<\/sup>+3a2<\/sup>b2<\/sup>c2<\/sup>=c<\/strong>4<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a2<\/sup>+b2<\/sup>=c2  <\/sup><\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, a6<\/sup>+b6<\/sup>+3a2<\/sup>b2<\/sup>c2<\/sup>=c4<\/sup><\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7= a6<\/sup>+b6<\/sup>+3a2<\/sup>b2<\/sup>c2<\/sup><\/p>\n\n\n\n

            =(a2<\/sup>)3<\/sup>+(b2<\/sup>)3<\/sup>+3a2<\/sup>b2<\/sup>c2<\/sup><\/p>\n\n\n\n

            =(a2<\/sup>+b2<\/sup>)3<\/sup>-3a2<\/sup>.b2<\/sup>(a2<\/sup>+b2<\/sup>)+ 3a2<\/sup>b2<\/sup>c2<\/sup><\/p>\n\n\n\n

            =(c2<\/sup>)3<\/sup>-3a2<\/sup>b2(<\/sup>c)2<\/sup>+3a2<\/sup>b2<\/sup>c2<\/sup><\/p>\n\n\n\n

                <\/sup>=c6<\/sup><\/p>\n\n\n\n

    =\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e7\u09e9\u0964 x+1\/x=4 \u09b9\u09b2\u09c7, \u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0 \u09af\u09c7, x3<\/sup>+1\/x3<\/sup>=52<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, x+1\/x=4<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09ae\u09be\u09a8 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09af\u09c7, x3<\/sup>+1\/x3<\/sup>=52<\/p>\n\n\n\n

\u09ac\u09be\u09ae\u09aa\u0995\u09cd\u09b7= x3<\/sup>+1\/x3<\/sup><\/p>\n\n\n\n

            = (x)3<\/sup>+(1\/x)3<\/sup><\/p>\n\n\n\n

                <\/sup>=(x+1\/x)3<\/sup>-3.x.1\/x(x+1\/x)<\/p>\n\n\n\n

            =(4)3<\/sup>-3(4)<\/p>\n\n\n\n

            =64-12<\/p>\n\n\n\n

            =52     <\/p>\n\n\n\n

   =\u09a1\u09be\u09a8\u09aa\u0995\u09cd\u09b7 (\u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4)<\/p>\n\n\n\n

\u09e7\u09ea\u0964 a-1\/a=5 \u09b9\u09b2\u09c7, a3<\/sup>-1\/a3<\/sup>  \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09a4?<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

\u09a6\u09c7\u0993\u09af\u09bc\u09be \u0986\u099b\u09c7, a-1\/a=5<\/p>\n\n\n\n

\u09aa\u09cd\u09b0\u09a6\u09a4\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf= a3<\/sup>-1\/a3<\/sup>  <\/p>\n\n\n\n

            =(a-1\/a)3<\/sup>+3.a.1\/a.(1-1\/a)<\/p>\n\n\n\n

            =53<\/sup>+3.5<\/p>\n\n\n\n

            =125+15        <\/p>\n\n\n\n

            =140<\/p>\n\n\n\n

\u09a8\u09bf\u09b0\u09cd\u09a8\u09c7\u09af\u09bc \u09ae\u09be\u09a8 140<\/p>\n\n\n\n

\u09e7\u09eb\u0964 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u0997\u09c1\u09a8\u09ab\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a8\u09af\u09bc \u0995<\/strong>\u09b0?<\/strong><\/p>\n\n\n\n

(\u0995) (a2<\/sup> + b2<\/sup> )(a4<\/sup> – a2<\/sup>b2<\/sup> + b4<\/sup> )  (\u0996) (ax – by)(a2<\/sup> x2<\/sup> + abxy + b2<\/sup> y2<\/sup> )<\/p>\n\n\n\n

(\u0997) (2ab2<\/sup> -1)(4a2<\/sup>b4<\/sup> + 2ab2<\/sup> +1)           (\u0998) (x2<\/sup> + a)(x4<\/sup> – ax2<\/sup> + a2<\/sup> )<\/p>\n\n\n\n

(\u0999) (7a + 4b)(49a2<\/sup> – 28ab +16b2<\/sup> )     (\u099a) (2a -1)(4a2<\/sup> + 2a +1)(8a3<\/sup> +1)<\/p>\n\n\n\n

(\u099b) (x + a)(x2<\/sup> – ax + a2<\/sup> )(x – a)(x2<\/sup> + ax + a2<\/sup> )<\/p>\n\n\n\n

(\u099c) (5a + 3b)(25a2<\/sup> -15ab +9b2<\/sup> )(125a3<\/sup> – 27b3<\/sup> )<\/p>\n\n\n\n

(\u0995) (a2<\/sup> + b2<\/sup> )(a4<\/sup> – a2<\/sup>b2<\/sup> + b4<\/sup> ) <\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983 (a2<\/sup> + b2<\/sup> )(a4<\/sup> – a2<\/sup>b2<\/sup> + b4<\/sup> )<\/p>\n\n\n\n

            =(a2<\/sup> + b2<\/sup> ){(a2<\/sup>)2<\/sup> – a2<\/sup>b2<\/sup> + (b2<\/sup>)2<\/sup> )<\/p>\n\n\n\n

            =( a2<\/sup>)3<\/sup> + (b2<\/sup>)3<\/sup><\/p>\n\n\n\n

                <\/sup>= a6<\/sup>+b6<\/sup><\/p>\n\n\n\n

 (\u0996) (ax – by)(a2<\/sup> x2<\/sup> + abxy + b2<\/sup> y2<\/sup> )<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(ax – by)(a2<\/sup> x2<\/sup> + abxy + b2<\/sup> y2<\/sup> )<\/p>\n\n\n\n

=(ax – by){(ax)2<\/sup> + abxy +( b y)2<\/sup> }<\/p>\n\n\n\n

=(ax)2<\/sup>+(bx)2<\/sup><\/p>\n\n\n\n

=a2<\/sup>x2<\/sup>+b2<\/sup>y2<\/sup><\/p>\n\n\n\n

(\u0997) (2ab2<\/sup> -1)(4a2<\/sup>b4<\/sup> + 2ab2<\/sup> +1)  <\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(2ab2<\/sup> -1)(4a2<\/sup>b4<\/sup> + 2ab2<\/sup> +1)  <\/p>\n\n\n\n

            =(2ab2<\/sup> -1){(2ab2<\/sup>)2<\/sup> + 2ab2<\/sup> +12<\/sup>}<\/p>\n\n\n\n

            =(2ab2<\/sup>)3<\/sup>-13<\/sup><\/p>\n\n\n\n

                <\/sup>=8a3<\/sup>b6<\/sup>-1<\/p>\n\n\n\n

(\u0998) (x2<\/sup> + a)(x4<\/sup> – ax2<\/sup> + a2<\/sup> )<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x2<\/sup> + a)(x4<\/sup> – ax2<\/sup> + a2<\/sup> )<\/p>\n\n\n\n

            =(x2<\/sup> + a){(x2<\/sup>)2<\/sup> – x2<\/sup> .a+ a2<\/sup> )<\/p>\n\n\n\n

            =(x2<\/sup>)3<\/sup>+(a)3<\/sup><\/p>\n\n\n\n

                <\/sup>=x6<\/sup>+a3<\/sup><\/p>\n\n\n\n

(\u0999) (7a + 4b)(49a2<\/sup> – 28ab +16b2<\/sup> )   <\/strong> <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(7a + 4b)(49a2<\/sup> – 28ab +16b2<\/sup> )<\/p>\n\n\n\n

            =(7a + 4b){(7a2<\/sup>)2<\/sup> \u2013 7a.4b +(4b2<\/sup>)2<\/sup>}<\/p>\n\n\n\n

            =(7a)3<\/sup>+(4b)3<\/sup><\/p>\n\n\n\n

            =343a3<\/sup>+64b3<\/sup><\/p>\n\n\n\n

 (\u099a) (2a -1)(4a2<\/sup> + 2a +1)(8a3<\/sup> +1)<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(2a -1)(4a2<\/sup> + 2a +1)(8a3<\/sup> +1)<\/p>\n\n\n\n

            =(2a -1){(2a)2<\/sup> + 2a.1 +12<\/sup>)(8a3<\/sup> +1)<\/p>\n\n\n\n

            ={(2a)3<\/sup>-(1)3<\/sup>}{8a3<\/sup>+1}<\/p>\n\n\n\n

            =(8a3<\/sup>-1)(8a3<\/sup>+1)<\/p>\n\n\n\n

            =(8a3<\/sup>)2<\/sup>-12<\/sup><\/p>\n\n\n\n

                <\/sup>=64a6<\/sup>-1<\/p>\n\n\n\n

(\u099b) (x + a)(x2<\/sup> – ax + a2<\/sup> )(x – a)(x2<\/sup> + ax + a2<\/sup> )<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(x + a)(x2<\/sup> – ax + a2<\/sup> )(x – a)(x2<\/sup> + ax + a2<\/sup> )<\/p>\n\n\n\n

            =(x3<\/sup> + a3<\/sup>)(x3<\/sup>-a3<\/sup>)<\/p>\n\n\n\n

            =x6<\/sup>-a6<\/sup><\/p>\n\n\n\n

(\u099c) (5a + 3b)(25a2<\/sup> -15ab +9b2<\/sup> )(125a3<\/sup> – 27b3<\/sup> )<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

(5a + 3b)(25a2<\/sup> -15ab +9b2<\/sup> )(125a3<\/sup> – 27b3<\/sup> )<\/p>\n\n\n\n

={(5a)3<\/sup>-(3b)3<\/sup>}(125a3<\/sup>-27b3<\/sup>)<\/p>\n\n\n\n

=(125a3<\/sup>+27b3<\/sup>)(125a3<\/sup>-27b3<\/sup>)<\/p>\n\n\n\n

=(125a3<\/sup>)2<\/sup>-(27b3<\/sup>)2<\/sup><\/p>\n\n\n\n

=15625a6<\/sup>-729b6<\/sup><\/p>\n\n\n\n

\u09e7\u09ec\u0964 \u0989\u09ce\u09aa\u09be\u09a6\u0995\u09c7 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a8 \u0995\u09b0\u0983<\/strong><\/p>\n\n\n\n

(\u0995) a3 <\/sup>+8         (\u0996) 8x3<\/sup> + 343   (\u0997) 8a4<\/sup> + 27ab3<\/sup><\/p>\n\n\n\n

(\u0998) 8x3<\/sup> +1        (\u0999) 64a3<\/sup> +125b3<\/sup>         (\u099a) 729a3<\/sup> + 64b3<\/sup>c6<\/sup><\/p>\n\n\n\n

(\u099b) 27a3<\/sup>b3<\/sup> + 64b3<\/sup>c3<\/sup>    (\u099c) 56x3<\/sup> +189 y3<\/sup><\/p>\n\n\n\n

(\u0995) a3 <\/sup>+8  <\/strong>      <\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

a3 <\/sup>+8<\/p>\n\n\n\n

            = a3 <\/sup>+23<\/sup><\/p>\n\n\n\n

                <\/sup>=(a+2)(a2<\/sup>-a*2+22<\/sup>)<\/p>\n\n\n\n

            =(a+2)(a2<\/sup>-2a+4)<\/p>\n\n\n\n

 (\u0996) 8x3<\/sup> + 343<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

8x3<\/sup> + 343<\/p>\n\n\n\n

            =(2x)3<\/sup> + 73<\/sup><\/p>\n\n\n\n

                <\/sup>=(2x+7){(2x)2<\/sup>-2x.7+72<\/sup>}<\/p>\n\n\n\n

            =(x+7)(4x2<\/sup>-14x+49)<\/p>\n\n\n\n

(\u0997) 8a4<\/sup> + 27ab<\/strong>3<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

8a4<\/sup> + 27ab3<\/sup><\/p>\n\n\n\n

                <\/sup>=a{8a3<\/sup> + 27b3<\/sup>}<\/p>\n\n\n\n

            =a{(2a)3<\/sup>+(3b)3<\/sup>}<\/p>\n\n\n\n

            =a{(2a+3b){(2a)2<\/sup>-2a.3+32<\/sup>)<\/p>\n\n\n\n

            =a(2a+3b)(4a2<\/sup>-6a+9)<\/p>\n\n\n\n

(\u0998) 8x3<\/sup> +1<\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

8x3<\/sup> +1<\/p>\n\n\n\n

            =(2x)3<\/sup> +13<\/sup>)<\/p>\n\n\n\n

                <\/sup>=(2X+1){(2x)2<\/sup>-2x.1+12<\/sup>}<\/p>\n\n\n\n

            =(2a+1)(4x2<\/sup>-21+1)<\/p>\n\n\n\n

(\u0999) 64a3<\/sup> +125b3<\/sup><\/strong><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

64a3<\/sup> +125b3<\/sup><\/p>\n\n\n\n

=(4a)3<\/sup> +(5b)3<\/sup><\/sub><\/p>\n\n\n\n

=(4a+5b){(4a)2<\/sup>-4a.5b+(5b)2<\/sup>)<\/p>\n\n\n\n

=(4a+5b)(16a2<\/sup>-20ab+25b2<\/sup>)<\/p>\n\n\n\n

(\u099a) 729a3<\/sup> + 64b3<\/sup>c<\/strong>6<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

729a3<\/sup> + 64b3<\/sup>c6<\/sup><\/p>\n\n\n\n

                <\/sup>=(9a)3<\/sup> + (4bc2<\/sup>)3<\/sup><\/p>\n\n\n\n

                <\/sup>=(9a-4bc2<\/sup>){(9a)2<\/sup>+9a.4bc2<\/sup>+(4bc2<\/sup>)2<\/sup>}<\/p>\n\n\n\n

            =(9a-4bc2<\/sup>)(81a2<\/sup>+361bc2<\/sup>+16b2<\/sup>c4<\/sup>)<\/p>\n\n\n\n

(\u099b) 27a3<\/sup>b3<\/sup> + 64b3<\/sup>c<\/strong>3<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

27a3<\/sup>b3<\/sup> + 64b3<\/sup>c3<\/sup><\/p>\n\n\n\n

=b3<\/sup>{(3 a)3<\/sup> + (4c)3<\/sup>}<\/p>\n\n\n\n

=b3<\/sup>(3a+4c){(3a)2<\/sup>-3a.4c+(4c)2<\/sup>}<\/p>\n\n\n\n

= b3<\/sup>(3a+4c){(9a2<\/sup>-12ac+16c2<\/sup>)<\/p>\n\n\n\n

 (\u099c) 56x3<\/sup> +189 y<\/strong>3<\/strong><\/sup><\/p>\n\n\n\n

\u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983<\/p>\n\n\n\n

56x3<\/sup> +189 y3    <\/sup><\/p>\n\n\n\n

            =7(8x3<\/sup> +27 y3<\/sup>)<\/p>\n\n\n\n

            =7{(2x)3<\/sup>-(3y3<\/sup>}<\/p>\n\n\n\n

            =7(2x-3y)({(2x)2<\/sup>+2x.3y+(3y)2<\/sup>}<\/p>\n\n\n\n

            =7(2x-3y)(4x2<\/sup>+6xy+9y2<\/sup>)<\/p>\n\n\n\n

\n\n\n\n
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tags: <\/em>Bangladesh, Bangla, Bengali, Class 8\/JSC math BD, Class eight math solution bd, class 8 math pdf download, \u0985\u09b7\u09cd\u099f\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf\u09b0 \u0997\u09a3\u09bf\u09a4 \u09b8\u09ae\u09be\u09a7\u09be\u09a8\u0983 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ea.\u09e8 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09df \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u0964 \u0998\u09a8\u09ab\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u0985\u09a8\u09c1\u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math Book Solution | Chapter 04 : Algebraic formulas and applications| Class 8 math book Online Solution in Bangla (BD) \u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997| \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e8: \u0998\u09a8\u09ab\u09b2\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u0985\u09a8\u09c1\u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4 – PDF \u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf […]<\/p>\n","protected":false},"author":1,"featured_media":4919,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[36],"tags":[37,38],"class_list":["post-4984","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-eight-8","tag-class-8","tag-class-eight"],"yoast_head":"\n\u09ea\u09b0\u09cd\u09a5 \u0985\u09a7\u09cd\u09af\u09be\u09df\u0983 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09ac\u09b2\u09bf \u0993 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 | \u0985\u09a8\u09c1\u09b6\u09c0\u09b2\u09a8\u09c0 \u09ea.\u09e8 | \u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf - Study Zone BD<\/title>\n<meta name=\"description\" content=\"\u09ee\u09ae \u09b6\u09cd\u09b0\u09c7\u09a3\u09bf \u0997\u09a3\u09bf\u09a4 \u09ac\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u09ae\u09be\u09a7\u09be\u09a8 | Class Eight (08) Math Book Solution. 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