An equivalent expression gives the same value for every input. When a sum has different powers of one variable, combine like terms: terms with exactly the same variable part. Add or subtract the numbers in each group, keeping its power. A tempting slip is to find the right numbers but attach them to the wrong powers.
Hints
- Hint 1
A coefficient is the number multiplying a variable part. Find the terms whose variable part is . What happens when you combine their coefficients, including the minus sign?
- Hint 2
The terms with form a separate group. Add their coefficients, then keep that result separate from the result because the powers don't match.
Step-by-step
Combine like terms
Step 1Combine the squared terms
Like terms have the same variable and power. Here and match. Add their coefficients, the numbers multiplying , including the minus sign:
Only combine terms with the same power of .
- Step 2
Combine the terms with
The and terms both have to the first power, so add their coefficients:
Keep separate from ; their powers don't match.
- Step 3
Check the complete rewrite
Your two groups give . To check, replace with in both expressions and type and in Desmos. The curves overlap across the window, matching your algebra. So the equivalent expression is . Choice D.