Question

which expressions are equivalent to (3x + 3(x + y))?

choose all answers that apply:

a (6x + 3y)

b (3(x + x + y))

c (3xy)

Explanation:

Expand the given expression

Using the Distributive Property knowledge point

$$ 3x + 3(x + y) = 3x + 3x + 3y $$

Combine like terms

Using the Simplifying Expressions knowledge point

$$ 3x + 3x + 3y = (3 + 3)x + 3y = 6x + 3y $$

Factor the original expression

Using the Equivalent Expressions knowledge point

$$ 3x + 3(x + y) = 3[x + (x + y)] = 3(x + x + y) $$

Evaluate the given options

Using the Equivalent Expressions knowledge point

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Answer:

• (A) \(6x + 3y\) (Correct answer)
• (B) \(3(x + x + y)\) (Correct answer)
• (C) \(3xy\)