Appendix A - A.2 - Formulas and Equations - Exercises - Page 540: 11

$2a^2 + 2b^2$

By using the FOIL method, we multiply the first, outside, inside, and the last element of each bracket and we add them. So, $(a+b)^2 + (a-b)^2=(a+b)\times (a+b) + (a-b)\times (a-b) = a^2+2ab+b^2 + a^2-2ab+b^2 = 2a^2 + 2b^2$