An equivalent expression has the same value for every . If both terms contain the same parentheses, treat those parentheses as a shared factor: add the numbers in front and keep the parentheses together. Distributing only the first term drops part of the expression. You can check a rewrite in Desmos by graphing both forms and looking for complete overlap.
Hints
- Hint 1
Both terms contain the exact same . Treat the whole parenthesis as one common factor, like a single object. Which numbers count how many copies of it you have?
- Hint 2
An equivalent expression gives the same value for every . Graph the original and your factored rewrite in Desmos. If their lines overlap, what does that tell you about the rewrite?
Step-by-step
Factor the repeated parentheses
Step 1Pull out the shared factor
The common factor is the whole , because it appears in both terms. Add the numbers multiplying the repeated parentheses, and leave the parentheses intact. Use the distributive property backward:
- Step 2
Check the rewrite in Desmos
Type , then . Toggle the second graph off and on: the line doesn't move. The two forms are equivalent, meaning they give the same value for every .
- Step 3
Add the numbers in front
Add , keeping the entire parentheses attached:
The coefficient multiplies all of . So the expression on the right is equivalent to the original. Choice D.