Question

What is (a-b)2+(a+b)2

Answer 1

`2*(a^(2) + b^(2))`

Explanation:

Step 1:

We know that

`(a+b)^(2) = a^(2) + b^(2) + 2ab\\(a-b)^(2) = a^(2) + b^(2) -2ab\\`

Step 2:

Here

`(a+b)^(2) + (a-b)^(2) = a^(2) + b^(2) +2*a*b +a^(2) +b^(2) - 2*a*b`

on simplification,

`(a+b)^(2) + (a-b)^(2) = 2*(a^(2) + b^(2))`

Answer 2

2a^2 +2b^2

Explanation:

Expand the squares and collect terms.

(a -b)^2 +(a +b)^2 = (a^2 -2ab +b^2) +(a^2 +2ab +b^2) = 2a^2 +2b^2