Question

Factorize each of the following expression:
a⁴ − 16b⁴

Answer 1

$$\begin{gathered} a^4-16b^4=a^4-2^4{b}^4=(a^2{)}^2-(2^2{b}^2{)}^2 \\ =(a^2-2^2{b}^2)(a^2+2^2{b}^2) \\ =[a^2-(2b{)}^2\left]\right(a^2+4b^2) \\ =(a-2b\left)\right(a+2b\left)\right(a^2+4b^2) \end{gathered}$$