Basic Algebra Formula | With Example

Algebra formulas are short rules that let you simplify expressions and solve equations without starting from scratch each time. The ones below are the ones students use most often.

Identity 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
(a − b)³ = a³ − 3a²b + 3ab² − b³

Distributive law

a(b + c) = ab + ac. Example: 3(x + 4) = 3x + 12.

Commutative and associative properties

Commutative: a + b = b + a, and a × b = b × a. Associative: (a + b) + c = a + (b + c), and (a × b) × c = a × (b × c). Order and grouping do not change the result here.

Exponent rules

aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1, where a ≠ 0.

Linear and quadratic formulas

A linear equation ax + b = 0 has solution x = −b / a. A quadratic equation ax² + bx + c = 0 has solution x = (−b ± √(b² − 4ac)) / 2a.

Learn more

For a video explanation of this topic, see Khan Academy Algebra course.