Question

Factorize each of the following expression:
4(xy + 1)² − 9(x − 1)²

Answer 1

$$\begin{gathered} 4(xy+1{)}^2-9(x-1{)}^2 \\ =\left[2\right(xy+1){]}^2-[3(x-1){]}^2 \\ =\left[2\right(xy+1)-3(x-1\left)\right]\left[2\right(xy+1)+3(x-1\left)\right] \\ =(2xy+2-3x+3)(2xy+2+3x-3) \\ =(2xy-3x+5)(2xy+3x-1) \end{gathered}$$