Question

which expressions are equivalent to \\(2(4f + 2g)\\)?

choose 3 answers:

a \\(8f + 2g\\)

b \\(2f(4 + 2g)\\)

c \\(8f + 4g\\)

d \\(4(2f + g)\\)

e \\(4f + 4f + 4g\\)

Explanation:

Apply the distributive property

Using the Distributive Property knowledge point

$$ 2(4f + 2g) = 2 \cdot 4f + 2 \cdot 2g = 8f + 4g $$

Evaluate options A and B

Using the Equivalent Expressions knowledge point

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Evaluate option C

Using the Equivalent Expressions knowledge point

$$ \text{Option C: } 8f + 4g = 8f + 4g $$

Evaluate option D

Using the Distributive Property and Equivalent Expressions knowledge points

$$ 4(2f + g) = 4 \cdot 2f + 4 \cdot g = 8f + 4g $$

Evaluate option E

Using the Simplifying Expressions and Equivalent Expressions knowledge points

$$ 4f + 4f + 4g = (4 + 4)f + 4g = 8f + 4g $$

Answer:

• (A) \(8f + 2g\)
• (B) \(2f(4 + 2g)\)
• (C) \(8f + 4g\) (Correct answer)
• (D) \(4(2f + g)\) (Correct answer)
• (E) \(4f + 4f + 4g\) (Correct answer)