Factorize: 8a^3 + 27b^3 + 36a^2b + 54ab^2 - Vidyadip

Question

Factorize:
$8a^3 + 27b^3 + 36a^2b + 54ab^2$

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Answer

$8 a^3+27 b^3+36 a^2 b+54 a b^2$
$=(2 a)^3+(3 b)^3+3 \times(2 a)^2 \times 3 b+3 \times(2 a)(3 b)^2$
$=(2 a+3 b)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(2 a+3 b)(2 a+3 b)(2 a+3 b)$
$\therefore 8 a^3+27 b^3+36 a^2 b+54 a b^2$
$=(2 a+3 b)(2 a+3 b)(2 a+3 b)$

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