Which expression is equivalent to ?
For questions asking for an equivalent expression with like terms, first confirm the variable parts match exactly (same variable and exponent), then ignore the variables and operate only on the coefficients. Perform the indicated operation (add or subtract) on the numbers, keep the common variable part attached, and then match your simplified term to the correct answer choice. This approach is fast and avoids sign errors if you pay close attention to the order of subtraction.
Hints
Look at what is the same
Both terms have . What part of the terms is actually changing when you subtract them?
Focus on the coefficients
Think of the expression as . What do you get when you subtract from ?
Combine like terms correctly
After you subtract the coefficients, remember to keep the variable part attached to the result.
Desmos Guide
Enter the expression to simplify
Type 12x^3 - 9x^3 into Desmos exactly as written. You can use any value for (for example, Desmos may automatically treat it as a function of ).
Check the simplified form
Click or tap on the expression line; Desmos will usually display a simplified form on the right side. Note the single-term expression Desmos shows that is equivalent to .
Step-by-step Explanation
Recognize like terms
Notice that both terms, and , have the same variable part . That means they are like terms and can be combined by operating on their numerical coefficients (the numbers in front).
Subtract the coefficients
Focus on the coefficients and . The expression is the same as because you are subtracting the coefficients of the like terms and keeping the same.
Compute the difference and rewrite the expression
Compute . So , which matches answer choice D.