Factorize: a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3 - Vidyadip

Question

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

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Answer

$a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
$= (ax)^3 - 3(ax)^2 \times b + 3(ax)b^2 - b^3$
$= (ax - b)^3 \big[\because a^3 - 3a^2b + 3ab^2 - b^3= (a - b)^3\big]$
$= (ax - b)(ax - b)(ax - b)$
$\therefore a^3x^3 - 3a^2bx^2 + 3ab^2x - b^3$
$= (ax - b)(ax - b)(ax - b)$

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