Factorise: 8 x^3+27 y^3+36 x^2 y+54 x y^2 - Vidyadip

Question

Factorise: $8 x^3+27 y^3+36 x^2 y+54 x y^2$

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Answer

The given expression can be written as
$(2 x)^3+(3 y)^3+3\left(4 x^2\right)(3 y)+3(2 x)\left(9 y^2\right)$
$=(2 x)^3+(3 y)^3+3(2 x)^2(3 y)+3(2 x)(3 y)^2$
$=(2 x+3 y)^3\left(\text { Using Identity }(x+y)^3=x^3+y^3+3 x y(x+y)\right)$
$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$
This is the required factorisation.

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