Question

x3 - 9y3– 3xy (x – y) -এর উৎপাদক বিশ্লেষণ করাে।​

Answer 1

$Given \: x^{3} - 9y^{3} - 3xy(x-y)$

$= x^{3} - 9y^{3} - 3x^{2}y + 3xy^{2}$

$= (x^{3} - 3x^{2}y + 3xy^{2} - y^{3} )- 8y^{3}$

$= (x-y)^{3} - ( 2y )^{3}$

/* By Algebraic Identity */

$\boxed{ \pink{ a^{3} - 3a^{2}b+3ab^{2} - b^{3}= (a-b)^{3}}}$

$=[ (x-y)-2y] [ (x-y)^{2} + (x-y)(2y)+(2y)^{2}]$

/* By Algebraic Identity */

$\boxed {\blue{a^{3} - b^{3} = (a-b)(a^{2}+ab+b^{2})}}$

$= ( x-3y)[ x^{2}-2xy+y^{2}+2xy-2y^{2}+4y^{2} ]$

$= (x-3y)( x^{2}-3y^{2} )$

Therefore.,

$\red{ x^{3} - 9y^{3} - 3xy(x-y)}$

$\green { = (x-3y)( x^{2}-3y^{2} )}$

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