Question

Factorize:
(a + b)³ − (a − b)³

Answer 1

$$\begin{gathered} {\left(\mathrm{a\; +\; b}\right)}^3-{\left(a-b\right)}^3=\left[\left(a+b\right)-\left(a-b\right)\right]\left[{\left(a+b\right)}^2+\left(a+b\right)\left(a-b\right)+{\left(a-b\right)}^2\right] \\ =\left(a+b-a+b\right)\left[a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right] \\ =2b\left(3a^2+b^2\right) \end{gathered}$$