Identify the pair of equivalent expressions.

Question

A. 3x + 2x and x^(2) (3+2)
B. 2x + 2 and 2 (x + 2)
C. 2 (x + 3) and 2x + 6
D. -3 (x + 2) and -3x - 3

Answer 1

To determine the pair of equivalent expressions, we will simplify each option:

A. \( 3x + 2x \) simplifies to \( 5x \).
\( x^2(3 + 2) \) simplifies to \( 5x^2 \).
They are not equivalent.

B. \( 2x + 2 \) cannot be simplified further.
\( 2(x + 2) \) simplifies to \( 2x + 4 \).
They are not equivalent.

C. \( 2(x + 3) \) simplifies to \( 2x + 6 \).
Therefore, \( 2(x + 3) \) and \( 2x + 6 \) are equivalent.

D. \( -3(x + 2) \) simplifies to \( -3x - 6 \).
\( -3x - 3 \) does not equal \( -3x - 6 \).
They are not equivalent.

The only pair of equivalent expressions is:

C. \( 2(x + 3) \) and \( 2x + 6 \).