Equivalent expressions
Equivalent expressions produce the same output for every input. The SAT asks you to rewrite one form into another—simplify, factor, expand, or restructure—and pick the match.
Core Idea
Two expressions are equivalent when they give the same value for every possible input. Your job is to pick the right algebraic move—distribute, combine, factor, or apply exponent rules—to transform what's given into the form that matches an answer choice.
Understanding
Most Equivalent Expressions questions ask you to rewrite a given expression so it matches one of the answer choices. The answer choices themselves tell you which direction to go.
If every choice is expanded and simplified, distribute and combine like terms. If the choices are in factored form, factor. If they involve radicals or fractional exponents, apply exponent rules.
Five core moves cover nearly every question in this topic:
- Distribute and combine like terms to simplify messy expressions
- Factor using GCF, difference of squares, or trinomial factoring
- Add, subtract, or multiply polynomials term by term
- Complete the square or factor to reveal a vertex, zeros, or other hidden structure
- Apply exponent rules to simplify rational exponents and radicals
When you're stuck, try plugging in a simple value like
Concept Guides
5Combine like terms and use the distributive property to rewrite expressions.
When you see parentheses and multiple terms, distribute any multipliers first, then group and combin
Factor polynomials (GCF, difference of squares, trinomials) and expand products.
Factoring rewrites an expression as a product. The SAT primarily tests three types: pulling out a GC
Add, subtract, and multiply polynomials.
Polynomial arithmetic follows the same rules as regular arithmetic—you just need to track each term
Rewrite expressions to reveal structure (e.g., factors/zeros).
Sometimes the SAT asks you to rewrite an expression in a specific form—vertex form, factored form, o
Use exponent rules and rewrite rational exponents in radical form (and vice versa).
Exponent rules let you rewrite products, quotients, and powers of same-base expressions. Rational ex