Question
5 Use greatest common factor and the distributive property to write and equivalent in factored form. \( 4(6 x+0) \) a. \( 10 x+4 \) b. \( 24 x+1 \) c. \( 24 x+0 \) d. \( 24 x \)
Ask by Wright Burns. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equivalent expression in factored form is \( 24x \).
Solution
1. Begin with the expression: \( 4(6x + 0) \).
2. Apply the distributive property:
\[
4(6x + 0) = 4 \cdot 6x + 4 \cdot 0
\]
3. Compute the multiplication:
\[
4 \cdot 6x = 24x \quad \text{and} \quad 4 \cdot 0 = 0
\]
4. Combine the results:
\[
24x + 0 = 24x
\]
5. The equivalent expression in factored form is \( 24x \).
The correct answer is: \( d. \, 24x \).
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Simplify this solution Beyond the Answer
Let’s jump into the world of factoring! When you see \( 4(6x + 0) \), it’s a great opportunity to use the distributive property. Here, you can distribute the 4 to both terms inside the parentheses, which would give you \( 4 \cdot 6x + 4 \cdot 0 = 24x + 0 \), simplifying down to just \( 24x \). Now, isn’t it interesting how the greatest common factor plays in? The number 4 is the GCF of \( 4(6x + 0) \), so this factoring exercise allies perfectly with both finding commonalities and distribution. Keep practicing, and factoring will be a breeze!
