Question
17. Use the Distributive Property, and combine like terms to write an equivalent expression simplest form. SHOW YOUR WORK! DO NOT PUT SPACES IN YOUR ANSWER! \( 3(2 x+4 y+2 z)+2(x+4 z) \) Type a response
Ask by Parsons Daniel. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(8x+12y+14z\)
Solution
1. Distribute the coefficients:
- \( 3(2x+4y+2z)=3\cdot2x+3\cdot4y+3\cdot2z=6x+12y+6z \)
- \( 2(x+4z)=2\cdot x+2\cdot4z=2x+8z \)
2. Combine the like terms:
- Combine the \( x \)-terms: \( 6x+2x=8x \)
- There is only one \( y \)-term: \( 12y \)
- Combine the \( z \)-terms: \( 6z+8z=14z \)
3. The equivalent expression in simplest form is:
\[
8x+12y+14z
\]
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Simplify this solution Mind Expander
Let's break this down step by step using the Distributive Property and then combine like terms: 1. Distribute \(3\) to each term inside the first set of parentheses: \(3(2x) + 3(4y) + 3(2z) = 6x + 12y + 6z\) 2. Distribute \(2\) to each term inside the second set of parentheses: \(2(x) + 2(4z) = 2x + 8z\) 3. Now combine the results: \(6x + 12y + 6z + 2x + 8z\) 4. Combine like terms: \((6x + 2x) + 12y + (6z + 8z) = 8x + 12y + 14z\) So, the equivalent expression in simplest form is: **8x+12y+14z**
