Question

Factorize:
2a³ + 16b³ − 5a − 10b

Answer 1

$$\begin{gathered} 2a^3+16b^3-5a-10b=2\left[a^3+8b^3\right]-5\left(a+2b\right) \\ =2\left[a^3+{\left(2b\right)}^3\right]-5\left(a+2b\right) \\ =2\left(a+2b\right)\left[a^2-a\times 2b+{\left(2b\right)}^2\right]-5\left(a+2b\right) \\ =2\left(a+2b\right)\left(a^2-2ab+4b^2\right)-5\left(a+2b\right) \\ =\left(a+2b\right)\left[2\left(a^2-2ab+4b^2\right)-5\right] \end{gathered}$$