Expressions: Expansion & Factoring
Master the art of "opening up" and "closing down" algebraic expressions — two inverse operations that form the backbone of SAT algebra.
1. Expansion & Factoring: Inverse Operations
Think of expansion and factoring as opposite directions on the same road:
| Expansion | Factoring |
|---|---|
| Multiply to remove parentheses | Rewrite as a product of factors |
| "Opens up" an expression | "Closes down" an expression |
| $3(x+4) \rightarrow 3x+12$ | $3x+12 \rightarrow 3(x+4)$ |
| Simplifies for calculation | Simplifies for solving equations |
Why both matter on the SAT: Expansion lets you simplify and compute. Factoring reveals structure, finds zeros, and simplifies rational expressions. You need both skills for a top score.
Interactive visualization — available in the full lesson