Question

Factorize each of the following expression:
49(a − b)² − 25(a + b)²

Answer 1

$$\begin{gathered} 49(a-b{)}^2-25(a+b{)}^2 \\ =\left[7\right(a-b){]}^2-[5(a+b){]}^2 \\ =\left[7\right(a-b)-5(a+b\left)\right]\left[7\right(a-b)+5(a+b\left)\right] \\ =(7a-7b-5a-5b)(7a-7b+5a+5b) \\ =(2a-12b)(12a-2b) \\ =2(a-6b)2(6a-b) \\ =4(a-6b)(6a-b) \end{gathered}$$