1. **State the problem:** Expand the expression $ (5x + 6y)^2 $. 2. **Formula used:** The square of a binomial is given by the formula $$ (a + b)^2 = a^2 + 2ab + b^2 $$ where $a = 5x$ and $b = 6y$. 3. **Apply the formula:** $$ (5x + 6y)^2 = (5x)^2 + 2 \times (5x) \times (6y) + (6y)^2 $$ 4. **Calculate each term:** $$ (5x)^2 = 25x^2 $$ $$ 2 \times (5x) \times (6y) = 60xy $$ $$ (6y)^2 = 36y^2 $$ 5. **Combine all terms:** $$ 25x^2 + 60xy + 36y^2 $$ 6. **Final answer:** $$ (5x + 6y)^2 = 25x^2 + 60xy + 36y^2 $$