Multiply
`5xy^(2) xx(3x^(2) +2xy ) " by " 5xy^(2)`

Answer

To solve the problem of multiplying \( 5xy^2 \) by \( (3x^2 + 2xy) \) and then multiplying the result by \( 5xy^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Distribute \( 5xy^2 \) to each term in the parentheses \( (3x^2 + 2xy) \)**:
\[ 5xy^2 \cdot (3x^2 + 2xy) = 5xy^2 \cdot 3x^2 + 5xy^2 \cdot 2xy \]

2. **Calculate the first term**:
\[ 5xy^2 \cdot 3x^2 = 15x^{1+2}y^{2} = 15x^3y^2 \]

3. **Calculate the second term**:
\[ 5xy^2 \cdot 2xy = 10x^{1+1}y^{2+1} = 10x^2y^3 \]

4. **Combine the results from the distribution**:
\[ 15x^3y^2 + 10x^2y^3 \]

5. **Now multiply the entire expression by \( 5xy^2 \)**:
\[ (15x^3y^2 + 10x^2y^3) \cdot 5xy^2 \]

6. **Distribute \( 5xy^2 \) to each term**:
\[ 15x^3y^2 \cdot 5xy^2 + 10x^2y^3 \cdot 5xy^2 \]

7. **Calculate the first term**:
\[ 15x^3y^2 \cdot 5xy^2 = 75x^{3+1}y^{2+2} = 75x^4y^4 \]

8. **Calculate the second term**:
\[ 10x^2y^3 \cdot 5xy^2 = 50x^{2+1}y^{3+2} = 50x^3y^5 \]

9. **Combine the final results**:
\[ 75x^4y^4 + 50x^3y^5 \]

### Final Answer:
\[ 75x^4y^4 + 50x^3y^5 \]