Factorize $a^{3} x^{3} - 3 a^{2} b x^{2} + 3 a b^{2} x - b^{3}$

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Solution

$a^{3} x^{3} - 3 a^{2} b x^{2} + 3 a b^{2} x - b^{3} = (a x)^{3} - 3 \times (a x)^{2} \times b + 3 \times a x \times (b)^{2} - (b)^{3} = (a x - b)^{3} = (a x - b) (a x - b) (a x - b)$

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