SAT Math skill page
Recognize when two algebra expressions say the same thing in different forms.
What this tests
Choose the form that exposes what the question asks for, then justify each rewrite with algebra. Equivalent expressions must agree throughout the permitted domain, not just at the values you happen to test.
Expand and combine like terms when you need to compare coefficients or constants. Factor when you need to reveal a common factor or a repeated group. If a question asks for the value of a group of terms, look for that whole group before trying to solve for each variable separately.
A single mismatch at a permitted input rules out equivalence. A few matching inputs, by themselves, do not prove that two expressions always agree. To confirm a choice, rewrite it into the original form or simplify both to the same form using valid operations. Treat numerical checks as a way to catch mistakes, not as a replacement for that reasoning.
For a rational expression, identify the inputs that make the original denominator zero before simplifying. Cancel only a common nonzero factor multiplying the entire numerator and denominator, not individual terms in a sum. Keep the original excluded inputs even if the simplified form no longer shows the canceled factor.
References: College Board SAT Math specifications: equivalent expressions and Paul's Online Notes at Lamar University: rational expressions. Guidance reviewed .
Dolphin practice questions
Avoid these traps
Two expressions are equivalent only if they have the same value for every allowed input, not just one convenient test value.
A factor outside parentheses multiplies every term inside, including each term following a minus sign.
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FAQ
They produce the same value for every input in their shared domain.
Testing can catch an error, but algebraic rewriting is the reliable proof because one matching input is not sufficient.
