Question

Ubtract the sum of a2−2ab+b2 and 2a2+2ab+b2 from the sum of a2−b2 and a2+ab+3b2

Answer 1

$\text{First sum:}\\\\(a^2-2ab+b^2)+(2a^2+2ab+b^2)=(a^2+2a^2)+(-2ab+2ab)+(b^2+b^2)=3a^2+2b^2\\\\\text{Second sum:}\\\\(a^2-b^2)+(a^2+ab+3b^2)=(a^2+a^2)+(ab)+(-b^2+3b^2)=2a^2+ab+2b^2\\\\\text{Difference:}\\\\(2a^2+ab+2b^2)-(3a^2+2b^2)=2a^2+ab+2b^2-3a^2-2b^2\\\\=(2a^2-3a^2)+(ab)+(2b^2-2b^2)=\boxed{-a^2+ab}$