which expression is equivalent to
The phrase “which expression is equivalent to” is a standard way, usually in math questions, of asking you to choose or create another expression that always has the same value as a given one, even though it may look different on the page.
What “equivalent expression” means
- Two expressions are equivalent if, for every possible value you plug into the variables, they give exactly the same result.
- They often look different: one might use parentheses, another might be expanded or simplified, but numerically they always match.
Example:
- 3(2y+4)3(2y+4)3(2y+4) and 6y+126y+126y+12 are equivalent, because if you distribute the 3 you get 6y+126y+126y+12, and both give the same value for every yyy.
How to find an equivalent expression
When a question says “Which expression is equivalent to … ?” , it is asking you to do one of these:
- Distribute or factor
- Distribute a factor into parentheses:
- 4(x+5)4(x+5)4(x+5) → 4x+204x+204x+20.
- Distribute a factor into parentheses:
* Or factor a common factor out (reverse direction):
* 6y−216y-216y−21 → 3(2y−7)3(2y-7)3(2y−7).
- Combine like terms
- Group and add/subtract terms with the same variable(s) and powers:
- 2g+3t+8g+6=10g+3t+62g+3t+8g+6=10g+3t+62g+3t+8g+6=10g+3t+6.
- Group and add/subtract terms with the same variable(s) and powers:
- Test with substitution (conceptual check)
- Pick a value for the variable, plug it into both expressions, and see if the results match.
- If they match for all values, the expressions are equivalent.
Why your question feels incomplete
The phrase “which expression is equivalent to” is usually followed by a specific expression, like:
- “Which expression is equivalent to 5(x−1)+75(x-1)+75(x−1)+7?”
- Answer: 5x+25x+25x+2, because 5(x−1)+7=5x−5+7=5x+25(x-1)+7=5x-5+7=5x+25(x−1)+7=5x−5+7=5x+2.
Right now, the exact expression to work with is missing from what you shared. To give a precise answer (the actual equivalent expression), the original expression is needed. If you reply with the full question (for example:
“Which expression is equivalent to 3(2x+4)−x3(2x+4)-x3(2x+4)−x?”),
then a step‑by‑step simplification and the correct equivalent form can be provided.