Question
Vhich expression shows \( 7+21 \) written as a product of two factors? \( 3(3+7) \) \( 7(1+3) \) \( 7(3+3) \) \( 3(1+7) \)
Ask by Rogers Parsons. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 7(1+3) \)
Solution
To determine which expression correctly represents \( 7 + 21 \) as a product of two factors, let's evaluate each option:
1. **Option A: \( 3(3 + 7) \)**
\[
3 \times (3 + 7) = 3 \times 10 = 30 \quad (\text{Not equal to } 28)
\]
2. **Option B: \( 7(1 + 3) \)**
\[
7 \times (1 + 3) = 7 \times 4 = 28 \quad (\text{Correct})
\]
3. **Option C: \( 7(3 + 3) \)**
\[
7 \times (3 + 3) = 7 \times 6 = 42 \quad (\text{Not equal to } 28)
\]
4. **Option D: \( 3(1 + 7) \)**
\[
3 \times (1 + 7) = 3 \times 8 = 24 \quad (\text{Not equal to } 28)
\]
**Conclusion:** The correct expression is **Option B: \( 7(1 + 3) \)**.
**Answer:**
\( 7(1+3) \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Let's break it down! The expression \( 7 + 21 \) can be simplified to \( 7 + 21 = 28 \). Now, to find a product of two factors that gives us 28, we can check each option. After examining the options, we can see that \( 7(3 + 3) \) becomes \( 7 \times 6 = 42 \), which isn't right. However, \( 7(1 + 3) \) simplifies to \( 7 \times 4 = 28\), matching our original expression perfectly. So, the correct expression that shows \( 7 + 21 \) as a product of two factors is \( 7(1 + 3) \).
