Solution 2.1:2e

We expand the two quadratics using the squaring rule, and then sum the result.

\displaystyle \qquad \begin{align}(a+b)^2+(a-b)^2 &= (a^2+2ab+b^2)+(a^2-2ab+b^2)\\ &= a^2+2ab+b^2+a^2-2ab+b^2 \\ &= a^2+a^2+2ab-2ab+b^2+b^2\\ &= 2a^2 +2b^2 \end{align}