Explanation

We know that, (a+b)² = a² + b² + 2ab

Now, we have,

(a+b)² + (a-b)²

= (a² + b² + 2ab) + [a² + (-b)² + 2a(-b)]

= a² + b² + 2ab + a² + b² - 2ab

= 2a² + 2b²

= 2(a²+b²)

Thus, we get,

(a+b)² + (a-b)² =     2(a²+b²).