Factorise
$8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}$

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Solution

$8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2} = {(2 a)}^{3} + {(3 b)}^{3} + 3 {(2 a)}^{2} (3 b) + 3 (2 a) {(3 b)}^{2} = {(2 a + 3 b)}^{3}$

Hence, factorisation of $8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}$ is ${(2 a + 3 b)}^{3}$ .

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Similar questions

Factorize $8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}$

Factorize $8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}$

(2 a - 3 b)^{3}

= 8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}

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