1. **State the problem:** Simplify and solve the expression $ (x + y)^2 - 10(x + y) + 25 $. 2. **Recognize the formula:** This expression resembles a quadratic in terms of $ (x + y) $. The general form is $ a^2 - 2ab + b^2 = (a - b)^2 $. Here, $ a = (x + y) $ and $ b = 5 $. 3. **Rewrite the expression:** $$ (x + y)^2 - 10(x + y) + 25 = (x + y)^2 - 2 \times 5 \times (x + y) + 5^2 $$ 4. **Apply the perfect square trinomial formula:** $$ = \left((x + y) - 5\right)^2 $$ 5. **Final simplified form:** $$ (x + y - 5)^2 $$ This means the original expression is a perfect square and equals zero when $ x + y - 5 = 0 $, or equivalently $ x + y = 5 $.