To determine which pairs of expressions are equivalent, let's simplify each pair:
-
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(x + 3) and 2x + 6:
- Expanding 2(x + 3): \[ 2(x + 3) = 2x + 6 \]
- These are equivalent.
-
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).
-
−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.