Factorize: a^3 x^3-3 a^2 b x^2+3 a b^2 x-b^3

Question

Factorize:
$a^3 x^3-3 a^2 b x^2+3 a b^2 x-b^3$

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Answer

$a^3 x^3-3 a^2 b x^2+3 a b^2 x-b^3$
$=(a x)^3-3(a x)^2 x b+3(a x) b^2-b^3$
$=(a x-b)^3\left[\because a^3-3 a^2 b+3 a b^2-b^3=(a-b)^3\right]$
$=(a x-b)(a x-b)(a x-b)$
$\therefore a^3 x^3-3 a^2 b x^2+3 a b^2 x-b^3$
$=(a x-b)(a x-b)(a x-b)$

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