Question

Simplify: $a^3{x}^3-3a^2{x}^{2}b+3a{b}^{2}x-b^3$

Answer 1

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

We know, ${(a-b)}^3=a^3-3a^{2}b+3a{b}^2-b^3$

Using this identity,

${\left(ax\right)}^3-3{\left(ax\right)}^{2}b+3\left(ax\right){\left(b\right)}^2-{\left(b\right)}^3$

$\Rightarrow {(ax-b)}^3$

$\therefore a^3{x}^3-3a^2{x}^{2}b+3a{b}^{2}x-b^3={(ax-b)}^3.$

Hence, the answer is ${(ax-b)}^3.$