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The image shows a homework problem related to the distributive property of multiplication over addition, asking to factor expressions. The problem specifically asks for factoring using the property, similar to the example provided.

Let's break it down step by step.

### Problem:
The task is to use the distributive property to factor the following expressions:

#### a. \( xy + y^2 \)
Here, we can factor out the common term \( y \):
\[
xy + y^2 = y(x + y)
\]

#### b. \( xy + x \)
Here, we can factor out the common term \( x \):
\[
xy + x = x(y + 1)
\]

#### c. \( a^2b + ab^2 \)
Here, we can factor out the common term \( ab \):
\[
a^2b + ab^2 = ab(a + b)
\]

Each expression is factored using the distributive property by identifying the common factors.

Would you like a more detailed explanation of any of the steps or an example with a different type of expression?

Here are some related questions to practice:
1. How would you factor \( 3x + 3y \)?
2. Can you apply the distributive property to factor \( a^2x + ax \)?
3. What is the factored form of \( pq + pr \)?
4. How do you factor \( 2x^2y + 4xy \)?
5. Can you use the distributive property to factor \( m^2n + mn^2 \)?

**Tip**: When factoring, always look for the greatest common factor (GCF) that can be factored out from all the terms.

Using the distributive property of multiplication over addition, factor the following expressions:

a. xy + y^2
b. xy + x
c. a^2b + ab^2

Learn how to factor algebraic expressions using the distributive property. Example problems include xy + y^2, xy + x, and a^2b + ab^2, with detailed solutions. Suitable for students in Grades 8-10.

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