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 $$ a^{3} b^{2}= $$

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UpStudy AI · Accepted Answer

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 $$ \boxed{-11} $$.
a. Coefficient of $$ a^{2} = 4 $$ b. Coefficient of $$ a^{3} b^{2} = -11 $$

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