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

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Solution

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

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

Since we know $(a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$

Therefore,

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

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

Hence , factorization of given expression is $(2 x + 3 y), (2 x + 3 y)$ and $(2 x + 3 y)$ .

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Similar questions

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

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

The value of $(2 x + 3 y)^{3}$ is __________.

8 x^{3} - 27 y^{3}

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