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Algebra Identities Cheat Sheet

By Dr. Iris Vaughan, Mathematics Editor·Published 1 September 2025·Last reviewed 15 April 2026

Every key algebraic identity — difference of squares, perfect square trinomials, sum and difference of cubes — with worked examples and conditions.

Key Formulas
(a+b)² = a²+2ab+b²
(a−b)² = a²−2ab+b²
(a+b)(a−b) = a²−b²
(a+b)³ = a³+3a²b+3ab²+b³
a³−b³ = (a−b)(a²+ab+b²)
a³+b³ = (a+b)(a²−ab+b²)

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