Question

Factorize:
a³ + 3a²b + 3ab² + b³ − 8

Answer 1

$$\begin{gathered} a^3+3a^{2}b+3a{b}^2+b^3-8=\left(a^3+b^3+3a^{2}b+3a{b}^2\right)-8 \\ =\left[a^3+b^3+3ab\left(a+b\right)\right]-8 \\ ={\left(a+b\right)}^3-2^3 \\ =\left(a+b-2\right)\left[{\left(a+b\right)}^2+2\left(a+b\right)+2^2\right] \\ =\left(a+b-2\right)\left[{\left(a+b\right)}^2+2\left(a+b\right)+4\right] \end{gathered}$$