Question 196·Easy·Equivalent Expressions
Which expression is equivalent to ?
For questions asking for an equivalent expression with the same variable and exponent in every term, first recognize they are like terms. Ignore the variable part, combine just the coefficients (being careful with negative signs), then reattach the unchanged variable and exponent. Finally, match your simplified form to the correct answer choice, watching for trap options that change the exponent or multiply instead of add.
Hints
Identify the like terms
All three terms involve the same variable and exponent. What do they all have in common: , , and ?
Focus on the coefficients
Since the variable part is the same in every term, just combine the numbers in front: , , and .
Combine carefully with signs
Compute , then take that result and add . Whatever number you get becomes the new coefficient of .
Desmos Guide
Compare numeric values for a sample p
In Desmos (graphing or scientific), pick a number for (for example, ) and type the original expression 2p^3 - 5p^3 + 4p^3 with that value substituted (e.g., 2(2)^3 - 5(2)^3 + 4(2)^3) to find its numeric value.
Test each answer choice
For the same value, compute each option (e.g., p^3, 11p^6, -7p^3, p^7 with ). The choice whose value matches the original expression’s value (and will keep matching for other values you try) is the equivalent expression.
Step-by-step Explanation
Recognize like terms
Look at each term: , , and . They all have the same variable part, , so they are like terms and can be combined by adding their coefficients (the numbers in front).
Add the coefficients
Take just the coefficients: , , and . Combine them:
- First do to get a new coefficient.
- Then add to that result. This gives the single coefficient that will go in front of .
Rewrite the simplified expression
Attach your combined coefficient from Step 2 to . That gives a single term of the form . This final term is the simplified expression equivalent to , which is .