An equivalent expression gives the same value for every . For a short expression with parentheses, distribute first, then combine like terms. Desmos can check the constant term: evaluate the original at , where every term containing vanishes. Watch the minus before parentheses because it changes both signs inside.
Hints
- Hint 1
Set to make every term containing equal . Evaluate the original in Desmos at ; the result is the constant term, the part without , in any equivalent expression.
- Hint 2
The distributive property says to multiply by both terms in . Then treat the minus before as multiplication by , so both signs inside that group change.
- Hint 3
Like terms have the same variable part. Group the terms containing together and the plain numbers together. The plain numbers should combine to the value you found in Desmos.
Step-by-step
Distribute and check the constant
Step 1Find the constant with Desmos
Type , then . Desmos prints . At , every term containing vanishes, so the constant term in an equivalent expression must be .
- Step 2
Distribute the 3
Multiply by both terms in the first parentheses:
- Step 3
Distribute the minus sign
The minus before means multiply each term inside by . In particular, subtracting gives :
- Step 4
Group like terms
Like terms have the same variable part. Put the terms containing in one group and the constants in another:
- Step 5
Combine the groups
Subtract the coefficients, , and use the constant found in Desmos: . The equivalent expression is . Choice C.