Question
5 from Unit 6 , Lesson 11 Find two different ways to rewrite \( 3 x y+6 y z \) using the distributive property.
Ask by Lewis Patel. in the United States
Feb 25,2025
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Answer
There are two ways to rewrite \( 3xy + 6yz \) using the distributive property:
1. **Factoring out \( 3y \):**
\[
3xy + 6yz = 3y(x + 2z)
\]
2. **Grouping and factoring:**
\[
3xy + 6yz = 3y(x + 2z)
\]
Both methods result in the same factored form.
Solution
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 in both terms.
2. **Factor out the common factor**: We can factor \( 3y \) out of the expression:
\[
3xy + 6yz = 3y(x + 2z)
\]
### Method 2: Grouping the terms differently
1. **Rearranging the terms**: We can also group the terms differently. 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 both terms:
\[
3xy + 6yz = 3y(x + 2z)
\]
### Summary of the two methods
Both methods lead to the same factored form:
\[
3xy + 6yz = 3y(x + 2z)
\]
Thus, we have successfully rewritten the expression \( 3xy + 6yz \) using the distributive property in two different ways, both resulting in the same final expression.
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Simplify this solution Beyond the Answer
One way to rewrite \( 3xy + 6yz \) using the distributive property is by factoring out the common factor of \( 3y \). This gives you \( 3y(x + 2z) \). You’ll notice that both terms in the original expression share \( 3y \), making it an ideal candidate for factoring. Another method involves factoring out the common factor \( 3y \) in a different arrangement by choosing to rewrite it as \( 3y \cdot x + 3 \cdot 2y \cdot z \). This emphasizes separating the coefficients from the variable components, making it clearer how \( 3 \) is a common factor in both terms before re-factoring it out.
