Factorise $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$
Factorise $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$
The given expression can be written as
$(2 x)^{3}+(3 y)^{3}+3\left(4 x^{2}\right)(3 y)+3(2 x)\left(9 y^{2}\right)$
$=(2 x)^{3}+(3 y)^{3}+3(2 x)^{2}(3 y)+3(2 x)(3 y)^{2}$
$=(2 x+3 y)^{3}$ (Using Identity $VI$)
$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$
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