Question

identify which expressions are equivalent to the given expression.
7(2x + 2)

which of the following is equivalent to the expression 7(2x + 2)? select all that apply.
a. 7x + 14 + 7x
b. 14x + 14
c. 14x + 5

Explanation:

Step1: Expand the given expression

Using the distributive property \(a(b + c)=ab + ac\), for \(7(2x + 2)\), we have \(7\times2x+7\times2 = 14x + 14\).

Step2: Analyze Option A

Simplify \(7x + 14 + 7x\). Combine like terms: \(7x+7x = 14x\), so it becomes \(14x + 14\), which matches the expanded form.

Step3: Analyze Option B

We already found the expanded form of \(7(2x + 2)\) is \(14x + 14\), so Option B matches.

Step4: Analyze Option C

The expression is \(14x + 5\), which is not equal to \(14x + 14\), so it does not match.

Answer:

A. \(7x + 14 + 7x\)
B. \(14x + 14\)