Question
Use the distributive property to write an equivalent expression. \[ 6(k+5) \]
Ask by Brooks Simmons. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Use the distributive property to write \( 6(k + 5) \) as \( 6k + 30 \).
Solution
To apply the **distributive property** to the expression \( 6(k + 5) \), you multiply the **6** by each term inside the parentheses:
\[
6(k) + 6(5)
\]
Now, perform the multiplication:
\[
6k + 30
\]
**Equivalent Expression:**
\[
6k + 30
\]
**Explanation:**
- **Distributive Property Formula:** \( a(b + c) = ab + ac \)
- **Applying to \( 6(k + 5) \):**
- Multiply **6** by **k**: \( 6k \)
- Multiply **6** by **5**: \( 30 \)
- **Combine the results:** \( 6k + 30 \)
This is the expression rewritten using the distributive property.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
When you apply the distributive property to the expression \( 6(k+5) \), you multiply 6 by each term inside the parentheses. This means you take \( 6 \times k \) and \( 6 \times 5 \), resulting in \( 6k + 30 \). So, the equivalent expression is \( 6k + 30 \). This method of distributing not only simplifies calculations but also showcases the beauty of algebraic expressions, revealing the hidden structure behind seemingly complex problems. It's like peeling back the layers of an onion—you uncover the essence of the equation beneath!
