Question

Factorize each of the following algebraic expression:
a² − 8ab + 16b² − 25c²

Answer 1

$$\begin{gathered} a^2-8ab+16b^2-25c^2 \\ =(a^2-8ab+16b^2)-25c^2 \\ =[a^2-2\times a\times 4b+(4b{)}^2]-25c^2 \\ =(a-4b{)}^2-(5c{)}^2 \\ =[(a-4b)-5c\left]\right[(a-4b)+5c] \\ =(a-4b-5c\left)\right(a-4b+5c) \end{gathered}$$