1. **Problem statement:** Simplify the expression $(-5q^2 + 3p - 2q + p^2) + (4p + q + pq)$. 2. **Formula and rules:** To simplify, combine like terms. Like terms have the same variables raised to the same powers. Addition is commutative and associative, so we can rearrange and group terms. 3. **Step-by-step simplification:** - Group like terms: $(-5q^2) + (3p + 4p) + (-2q + q) + p^2 + pq$ - Simplify each group: - $3p + 4p = 7p$ - $-2q + q = -q$ - So the expression becomes: $$-5q^2 + 7p - q + p^2 + pq$$ 4. **Final answer:** $$-5q^2 + p^2 + 7p + pq - q$$