Question

Factorize each of the following algebraic expression:
a² + 4b² − 4ab − 4c²

Answer 1

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