5 from Unit 6, Lesson 11 Find two different ways to rewrite \( 3 x y+6 y z \) using the distributive property.

To rewrite the expression \( 3xy + 6yz \) using the distributive property, we can approach it in two different ways. ### Method 1: Factoring out the common factor 1. **Identify the common factor**: In the expression \( 3xy + 6yz \), we can see that \( 3y \) is a common factor. 2. **Factor out the common factor**: We can factor \( 3y \) out of both terms: \[ 3xy + 6yz = 3y(x + 2z) \] ### Method 2: Grouping the terms differently 1. **Group the terms**: We can also group the terms in a different way. Let's factor out \( 3z \) from the second term: \[ 3xy + 6yz = 3xy + 3(2yz) \] 2. **Factor out \( 3y \)**: Now we can factor out \( 3y \) from the entire expression: \[ 3y(x + 2z) \] ### Summary of the two methods 1. From Method 1, we have: \[ 3y(x + 2z) \] 2. From Method 2, we also arrive at: \[ 3y(x + 2z) \] Both methods yield the same factored form, but they illustrate different approaches to applying the distributive property.