Identify the pair of equivalent expressions.(1 point)

Question

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.