Question

Factorize the following expression:

$4(x+y)-6{(x+y)}^2$

Answer 1

Factorizing the given expression:

$$\begin{gathered} 4(x+y)-6{(x+y)}^2 \\ =2\times 2(x+y)-2\times 3{(x+y)}^2 \\ =2(x+y)[2-3(x+y\left)\right][Bytaking2(x+y)common] \\ =2(x+y)(2-3x-3y) \end{gathered}$$

Hence, after factorizing, we get $4(x+y)-6{(x+y)}^2=2(x+y)(2-3x-3y).$