Question

do not use the calculator for this question.

which of the following expressions applies the distributive property to factor out the greatest common factor from the expression (35 + 63)?

a. (7 \cdot 5 + 3 \cdot 21)
b. (5(7 + 13))
c. (5(7 + 12) + 3)
d. (7(5 + 9))

Explanation:

⚡ Using what you learned: using properties of operations

Step 1: Find the Greatest Common Factor (GCF)

Find the GCF of \( 35 \) and \( 63 \):

• Factors of \( 35 \): \( 1, 5, 7, 35 \)
• Factors of \( 63 \): \( 1, 3, 7, 9, 21, 63 \)

$$ \text{GCF}(35, 63) = 7 $$

Step 2: Rewrite each term

Express each term as a product of the GCF and another factor:

$$ 35 = 7 \cdot 5 $$

$$ 63 = 7 \cdot 9 $$

Step 3: Apply the distributive property

Factor out the GCF from the expression:

$$ 35 + 63 = 7(5 + 9) $$

Answer:

D (which is \( 7(5 + 9) \))