Equivalent expressions have the same value for every allowed input. Expansion, factoring and exponent rules can change the form while preserving that value.
Key Rules
Distribute a factor to every term inside parentheses.
Expand a squared sum as two multiplied binomials, including the middle term.
When canceling a factor in a fraction, keep any original restrictions on the denominator.
Common Mistakes to Avoid
Treating (a + b)² as a² + b².
Canceling a term across addition instead of a common factor.
SAT Strategy Tips
→Use substitution as a quick way to disprove a proposed identity.
→Factored and expanded forms highlight different features; choose the useful one.
Example Question
Which expression is equivalent to (x + 3)²?
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