The value of (x + y)² + (x - y)² is equal to:

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Accepted Answer

We need to simplify the expression (x + y)² + (x - y)².

Step 1: Expand each square using the formula (a ± b)² = a² ± 2ab + b².

(x + y)² = x² + 2xy + y²  
(x - y)² = x² - 2xy + y²

Step 2: Add the two expansions:  
(x + y)² + (x - y)² = (x² + 2xy + y²) + (x² - 2xy + y²)  
= x² + 2xy + y² + x² - 2xy + y²

Step 3: Combine like terms:  
= x² + x² + 2xy - 2xy + y² + y²  
= 2x² + 0 + 2y²  
= 2(x² + y²)

Therefore, the value of (x + y)² + (x - y)² is 2(x² + y²).

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