Find the value

Question:

Find the value.

$8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

Solution:

$=(2 x)^{3}+(3 y)^{3}+3 \times(2 x)^{2} \times 3 y+3 \times(2 x)(3 y)^{2}$

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

$\left[\therefore a^{3}+b^{3}+3 a^{2} b+3 a b^{2}=(a+b)^{3}\right]$

$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$

$\therefore 8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$

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