Factorise

Question:

Factorise

$8(x+y)^{3}-27(x-y)^{3}$

 

Solution:

$8(x+y)^{3}-27(x-y)^{3}$

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

$=(2 x+2 y-3 x+3 y)\left[4(x+y)^{2}+9(x-y)^{2}+6\left(x^{2}-y^{2}\right)\right]$

$=(-x+5 y)\left[4\left(x^{2}+y^{2}+2 x y\right)+9\left(x^{2}+y^{2}-2 x y\right)+6\left(x^{2}-y^{2}\right)\right]$

$=(-x+5 y)\left[4 x^{2}+4 y^{2}+8 x y+9 x^{2}+9 y^{2}-18 x y+6 x^{2}-6 y^{2}\right]$

$=(-x+5 y)\left(19 x^{2}+7 y^{2}-10 x y\right)$

 

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