Simplify the expression and answer the following: a. What is the resulting coefficient of \( a^{2} \) ? b. What is the resulting coefficient of \( a^{3} b^{2} \) ? \( \left(15 a^{2}-a^{3} b^{2}-9 b^{3}\right)+\left(-10 a^{3} b^{2}-11 a^{2}-b^{2}+25 a\right. \) a. Coefficient of \( a^{2}= \) b. Coefficient of \( a^{3} b^{2}= \)

We start with the given expression: \[ \left(15 a^{2}-a^{3} b^{2}-9 b^{3}\right)+\left(-10 a^{3} b^{2}-11 a^{2}-b^{2}+25 a\right) \] **Step 1: Remove Parentheses and Write All Terms** \[ 15 a^{2} - a^{3} b^{2} - 9 b^{3} - 10 a^{3} b^{2} - 11 a^{2} - b^{2} + 25 a \] **Step 2: Combine Like Terms** - For \(a^{2}\) terms: \[ 15 a^{2} - 11 a^{2} = 4 a^{2} \] - For \(a^{3} b^{2}\) terms: \[ -a^{3} b^{2} - 10 a^{3} b^{2} = -11 a^{3} b^{2} \] - The remaining terms do not have like terms: \[ - 9 b^{3}, \quad -b^{2}, \quad 25 a \] The simplified expression is: \[ 4 a^{2} - 11 a^{3} b^{2} - 9 b^{3} - b^{2} + 25 a \] **Step 3: Answer the Questions** a. The coefficient of \( a^{2} \) is \( \boxed{4} \). b. The coefficient of \( a^{3} b^{2} \) is \( \boxed{-11} \).