Question

a2+b2=a square + b square +

Answer 1

a+2ab+b is answer of a2+b2
by your method a square+b square +2ab
and in that if their is (-)sign then a2-b2=a2+b2-2ab
this is your answer I hope it helps you

Answer 2

so,
 $a^{2} + b^{2}$ doesnt have a solution,
although there is a solution for $a^{2} - b^{2}$ which is,
$a^{2} - b^{2} = (a-b) (a+b)$ .
the other equation can be 
$(a+b)^2 = a^2 + 2ab + b^2$ and $(a-b)^2 = a^2 - 2ab - b^2$
hope it helps ! :)