The cue for like terms is a matching variable part, including its exponent. To find an equivalent expression, subtract the coefficients and keep the shared variable part unchanged. Desmos can check your rewrite: equivalent expressions draw overlapping curves, not curves that meet at only one point. The tempting trap is to add the coefficients despite the minus sign.
Hints
- Hint 1
Two terms are like terms when they have the same variable part. You can treat each as one unit. Which numbers tell you how many of those units you have and how many to take away?
- Hint 2
A coefficient is the number multiplying a variable part. Keep the subtraction in order: take the second number of units away from the first. What stays unchanged about each unit?
Step-by-step
Combine like terms
Step 1Keep the shared variable part
Both terms contain , so they're like terms, terms with the same variable part. Keep unchanged while you group the numbers in front: . Type in Desmos. It draws the original curve, which you'll compare with your rewrite.
- Step 2
Subtract the coefficients
The coefficient is the number in front of . Subtract the coefficients in the given order:
so . Type below the original in Desmos. The curves overlap across the window, confirming the rewrite. The equivalent expression is . Choice D.