Question

which choice correctly shows how to use the distributive property to express the sum \\(8 + 14\\)?

\\(8 + 14 = 4(2 + 7)\\)
\\(8 + 14 = 2(4 + 7)\\)
\\(8 + 14 = 2 + (4)(7)\\)
\\(8 + 14 = 2(4)(7)\\)

Explanation:

Find the greatest common factor

Using the Greatest Common Factor knowledge point

$$
LATEXBLOCK0
$$

Apply the distributive property

Using the Distributive Property knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given options

We compare our derived expression with the choices:

• \(8 + 14 = 4(2 + 7)\) is incorrect because \(4(2+7) = 8 + 28 = 36\).
• \(8 + 14 = 2(4 + 7)\) is correct because \(2(4+7) = 8 + 14 = 22\).
• \(8 + 14 = 2 + (4)(7)\) is incorrect because \(2 + 28 = 30\).
• \(8 + 14 = 2(4)(7)\) is incorrect because \(2 \cdot 4 \cdot 7 = 56\).

Answer:

• (A) \(8 + 14 = 4(2 + 7)\)
• (B) \(8 + 14 = 2(4 + 7)\) (Correct answer)
• (C) \(8 + 14 = 2 + (4)(7)\)
• (D) \(8 + 14 = 2(4)(7)\)