Question

Factorize each of the following expression:
a⁴ − 16(b − c)⁴

Answer 1

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