Question

Factorize each of the following expression:
a⁴ − (2b + c)⁴

Answer 1

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