If (a-b)² = 16 and (a+b)² = 25, then 2a² + 2b² = ?

Explanation

We are given (a-b)^2=16 and (a+b)^2=25. Adding them gives

(a-b)^2+(a+b)^2=2a^2+2b^2.
Therefore 2a^2+2b^2=16+25=41. The cross terms +2ab and -2ab cancel automatically.