Equivalent Expressions
Simplifying expressions using factoring, exponent rules, and combining like terms
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Rewrite an expression in a different form — by expanding, factoring, or applying exponent and fraction rules.
Why this matters
The SAT tests five distinct types of algebraic manipulation. Each one requires a different technique — distributing, factoring, applying exponent laws, simplifying fractions, or matching coefficients.
The five patterns
Expand and Combine
Distribute, multiply out polynomials, and combine like terms. Straightforward — but one sign error and you're done.
›Factoring
Rewrite a polynomial as a product of simpler expressions. Know your GCF, difference of squares, and trinomial factoring cold.
›Exponent Rules
Simplify expressions using exponent laws — multiplying, dividing, negative exponents, and fractional exponents that are really radicals.
›Simplifying Fractions
Add, subtract, or simplify algebraic fractions. The catch: you need a common denominator or need to factor before canceling.
›Equating Coefficients
Find an unknown constant by matching the structure of two equivalent expressions. Expand one side, then line up corresponding terms.