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Equivalent-expression questions ask you to rewrite an expression in a different form that has the exact same value. It’s bookkeeping, not insight, but small sign errors turn easy points into misses. Three moves cover almost all of them.
Key takeaways
- Distribute: multiply through parentheses, watching signs.
- Combine like terms: add coefficients of matching variable parts.
- Factor: pull out the greatest common factor or reverse-FOIL.
- The trap is a dropped negative when distributing across a subtraction.
The three moves
Most equivalent-expression items are some mix of distributing, combining like terms, and factoring. Do them carefully and in order, and the matching answer falls out. The whole risk is sign-keeping, especially a minus sign in front of parentheses. (Factoring in particular pays off again on quadratics.)
-(3x - 4) = -3x + 4, not -3x - 4. A minus (or a negative multiplier) hits every term inside the parentheses. This is the most common slip on these questions.
Try one
Which expression is equivalent to 3(2x - 4) + 5x?
The method
- 1
Distribute everything
Multiply across every set of parentheses; carry the signs.
- 2
Combine like terms
Add coefficients of matching terms (x with x, constants with constants).
- 3
Factor if asked
Pull out the greatest common factor, or reverse-FOIL a quadratic.
Factoring patterns worth knowing cold
Harder items run the other direction: they hand you the multiplied-out form and ask for a factored equivalent. Three patterns cover nearly all of it, and the difference of squares is the one the SAT reuses most (it comes back on quadratics as instant roots).
| You see… | It factors to… |
|---|---|
| a common factor in every term: 6x^2 + 9x | 3x(2x + 3) |
| a difference of squares: a^2 - b^2 | (a + b)(a - b) |
| a perfect square trinomial: a^2 + 2ab + b^2 | (a + b)^2 |
Which expression is equivalent to 4x^2 - 25?
The plug-in-a-number check
Equivalent means equal for every value of x, which hands you a verification trick: pick a small number (say x = 2), evaluate the original expression, then evaluate the choices and keep the one that matches. Avoid x = 0 and x = 1, where too many wrong choices coincidentally agree. It’s slower than clean algebra, but it converts "I think" into a checked answer, and it works even when the expression looks ugly.
Drill distributing, combining, and factoring with a tutor that flags dropped signs.
Practice equivalent expressions →Frequently asked questions
- What are equivalent expressions on the SAT?
- Different algebraic forms of the same expression. They look different but have equal value for every input. You rewrite by distributing, combining like terms, and factoring.
- How do I rewrite an expression correctly?
- Distribute across all parentheses (carrying signs), combine like terms, and factor if the question asks. Keep careful track of negative signs throughout.
- What’s the most common equivalent-expressions mistake?
- Dropping a negative when distributing across a subtraction: for example, writing -(3x - 4) as -3x - 4 instead of -3x + 4. The negative applies to every term inside.
- Can I plug in a number to test equivalent expressions?
- Yes. Equivalent expressions agree for every input, so evaluate the original and each choice at a small value like x = 2 and keep the match. Avoid 0 and 1, where wrong choices often coincide with the right one.