Question

Identify the pair of equivalent expressions.(1 point)
Responses

2x+2
and 2(x+2)
2 x plus 2 and 2 times open paren x plus 2 close paren

2(x+3)
and 2x+6
2 times open paren x plus 3 close paren and 2 x plus 6

3x+2x
and x2(3+2)
3 x plus 2 x and x squared times open paren 3 plus 2 close paren

−3(x+2)
and −3x−3

Answer 1

To determine which pairs of expressions are equivalent, let's simplify each pair:

1. **2x + 2 and 2(x + 2)**:
- The expression 2(x + 2) can be expanded:
\[
2(x + 2) = 2x + 4
\]
- Thus, **2x + 2** is not equivalent to **2(x + 2)**.

2. **2(x + 3) and 2x + 6**:
- Expanding 2(x + 3):
\[
2(x + 3) = 2x + 6
\]
- These are equivalent.

3. **3x + 2x and x^2(3 + 2)**:
- Simplifying 3x + 2x:
\[
3x + 2x = 5x
\]
- Simplifying x^2(3 + 2):
\[
x^2(3 + 2) = x^2 \cdot 5 = 5x^2
\]
- Thus, **3x + 2x** is not equivalent to **x^2(3 + 2)**.

4. **−3(x + 2) and −3x − 3**:
- Expanding −3(x + 2):
\[
-3(x + 2) = -3x - 6
\]
- These are not equivalent.

The only pair of equivalent expressions is **2(x + 3)** and **2x + 6**.