If P + Q = R and P - Q = S, prove that `R^2 + S^2 = 2(P^2 + Q^2)`

Explanation

To prove that \( R^2 + S^2 = 2(P^2 + Q^2) \) given the equations \( P + Q = R \) and \( P - Q = S \), we can follow these steps:

### Step 1: Express \( R^2 \) and \( S^2 \) in terms of \( P \) and \( Q \)

Using the definitions of \( R \) and \( S \):
\[ R = P + Q \quad \text{and} \quad S = P - Q \]
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