Question

factorise this please help

Answer 1

27(x+y)³-8(x-y)³
=3³(x+y)³-2³(x-y)³
={3(x+y)}³-{2(x-y)}³
=(3x+3y)³-(2x-2y)³
Now since,
→a³-b³=(a-b)(a²+ab+b²)
:. putting value
→(3x+3y)³-(2x-2y)³={(3x+3y)-(2x-2y)}{(3x+3y)²+(3x+3y)(2x+2y)+(2x+2y)²}
Since,
→(a+b)²=a²+b²+2ab
:. Putting value
→(3x+3y)³-(2x-2y)³=(3x+3y-2x+2y){(9x²+9y²+18xy)+(3x+3y)(2x+2y)+(2x+2y)²}
Since,
→(a-b)²=a²+b²-2ab
:. Putting value
→(3x+3y)³-(2x-2y)³=(3x+3y-2x+2y){(9x²+9y²+18xy)+(3x+3y)(2x+2y)+(4x²+4y²+8xy)}
→(3x+3y)³-(2x-2y)³=(3x+3y-2x+2y)(9x²+9y²+18xy+6x²+6xy+6xy+6y²+4x²+4y²+8xy)
→(3x+3y)³-(2x-2y)³=(x+5y)(19x²+19y²+38xy)
:.27(x+y)³-8(x-y)³=(5y+x)(19x²+19y²+38xy)
(ÆÑẞWĒR)