An equivalent expression has the same value for every value of its variable. A number outside parentheses signals a short rewrite: multiply it by each term inside, then combine the numbers without a variable. You can check your rewrite in Desmos by setting the variable to one. The main trap is leaving one term inside the parentheses untouched.
Hints
- Hint 1
The distributive property means the multiplies each term inside the parentheses. What do you get from and from before bringing down the ?
- Hint 2
Equivalent expressions give the same output for the same input. If you check the original at in Desmos, how can you use its output to check your rewrite after combining the constants?
Step-by-step
Distribute, then check the rewrite
Step 1Multiply through the parentheses
The distributive property says the outside multiplies every term inside. Multiply by both and before bringing down the . Distribute:
- Step 2
Check one input in Desmos
An equivalent expression must give the same output as the original at any input, so check the original at . In Desmos, type , using for the question's , then type . Desmos prints .
- Step 3
Combine the constants
Keep and combine the constant terms and :
Adding makes less negative. At , , which agrees with the Desmos check. The equivalent expression is . Choice A.