Question

Use the image to answer the question.

An illustration shows that one rectangular tile equals a, another rectangular tile equals b, and a square tile equals positive 1.

Model each pair of algebraic expressions using the key. Which of the following are equivalent expressions?

(1 point)
Responses

(a+3)+b
and 3(a+b)

left parenthesis a plus 3 right parenthesis plus b and 3 left parenthesis a plus b right parenthesis

2a+2b+1
and 2(a+b+1)

2 a plus 2 b plus 1 and 2 left parenthesis a plus b plus 1 right parenthesis

a+2b+2
and 2a+b+2

a plus 2 b plus 2 and 2 a plus b plus 2

2a+2b+1
and 2(a+b)+1

2 a plus 2 b plus 1 and 2 left parenthesis a plus b right parenthesis plus 1
Remaining Attempts : 3

Answer 1

Only the fourth pair is equivalent.

Reasoning:
- (a+3)+b = a+b+3, while 3(a+b) = 3a+3b → not equal in general.
- 2a+2b+1 vs 2(a+b+1) = 2a+2b+2 → not equal.
- a+2b+2 vs 2a+b+2 → equal only if a = b, not identically equal.
- 2a+2b+1 = 2(a+b)+1 exactly, so they are equivalent.