Question

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

Answer 1

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

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

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

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

$=(2x-2y-3x-3y{)}^2$
$=(-x-5y{)}^2$
$=(x+5y{)}^2$

Hence, $4(x-y{)}^2-12(x-y\left)\right(x+y)+9(x+y{)}^2=(x+5y{)}^2$