Multiply (3xy + 2y) by 5xy.

Answer

To solve the problem of multiplying the expression (3xy + 2y) by 5xy, we will follow these steps:

### Step-by-Step Solution:

1. **Write down the expression to be multiplied:**
\[ (3xy + 2y) \times 5xy \]

2. **Distribute 5xy to each term inside the parentheses:**
\[ = 5xy \times 3xy + 5xy \times 2y \]

3. **Multiply the first term:**
- Multiply the coefficients: \(5 \times 3 = 15\)
- For the variables, \(xy \times xy\):
- The power of \(x\) is \(1 + 1 = 2\)
- The power of \(y\) is \(1 + 1 = 2\)
- So, \(xy \times xy = x^2y^2\)
- Therefore, \(5xy \times 3xy = 15x^2y^2\)

4. **Multiply the second term:**
- Multiply the coefficients: \(5 \times 2 = 10\)
- For the variables, \(xy \times y\):
- The power of \(x\) remains \(1\) (since there is no \(x\) in \(y\))
- The power of \(y\) is \(1 + 1 = 2\)
- So, \(xy \times y = xy^2\)
- Therefore, \(5xy \times 2y = 10xy^2\)

5. **Combine the results of both multiplications:**
\[ 15x^2y^2 + 10xy^2 \]

### Final Answer:
\[ 15x^2y^2 + 10xy^2 \]

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