Techniques

Contest algebra is not a test of how many formulas you can recall. It’s a test of whether you can look at an unfamiliar expression and recognize which of a dozen standard moves will open it up.

These articles cover those moves — from the factoring patterns and substitutions that solve most school-level problems, through to the polynomial identities, symmetric sums, complex numbers, and modular arithmetic that appear once the difficulty rises. The order they’re best learned in is laid out in Algebra Topics.