Question

Factorize:

$4(x-y{)}^2+12(x-y\left)\right(x+y)+9(x+y{)}^2$

Answer 1

$4(x-y{)}^2+12(x-y\left)\right(x+y)+9(x+y{)}^2$

$=\left[2\right(x-y){]}^2+2\times 2(x-y)\times 3(x+y)+[3(x+y){]}^2$

$[\text{Using the identity,}{a}^2+2\times a\times b+b^2=(a+b{)}^2]$

Here, $a=2(x-y)$, $b=3(x+y)$

$=\left[2\right(x-y)+3(x+y){]}^2$

$=(2x-2y+3x+3y{)}^2$

$=(5x+y{)}^2$