An equivalent expression has the same value for every . A number outside parentheses signals the distributive property: multiply it by each term inside. For a short expression, you can use Desmos to find the constant by evaluating at , then multiply to find the -term. Check the sign of each product before combining terms.
Hints
- Hint 1
The constant term is the part without . Set in the original expression: the -term disappears, leaving the constant. What value does Desmos give?
- Hint 2
The distributive property means the number outside parentheses multiplies every term inside. Multiply by to find the -term; don't drop the .
Step-by-step
Find the two terms
Step 1Find the constant
Type , then . Desmos prints . Setting removes the -term, so is the constant term, the part without . It's positive because multiplies two negative numbers.
- Step 2
Find the -term
The outside factor also multiplies the entire term. Multiply:
- Step 3
Put the terms together
By the distributive property, the outside factor multiplies both terms inside the parentheses. Put the -term and constant together: . The equivalent expression is . Choice C.