Question:
Find the value
$a^{3} x^{3}-3 a^{2} b x^{2}+3 a b^{2} x-b^{3}$
Solution:
$=(a x)^{3}-3(a x)^{2} \times b+3(a x) \times b^{2}-b^{3}$
$=(a x-b)^{3}$
$\left[\therefore a^{3}-b^{3}-3 a^{2} b+3 a b^{2}=(a-b)^{3}\right]$
$=(a x-b)(a x-b)(a x-b)$
$\therefore a^{3} x^{3}-3 a^{2} b x^{2}+3 a b^{2} x-b^{3}$
$=(a x-b)(a x-b)(a x-b)$