Question

show that if 2(a+b)² =(a+b)² ,then a=b

Answer 1

subracting (a+b)^2  from both sides

(a+b)^2 = 0

therefore

a+b = 0

therfore 

a=-b

Answer 2

$2(a+b)^2-(a+b)^2=0$
$(a+b)^2=0$
$a+b=0$
$a=-b$
if $a=b$
then $a=b=0$