📖 Math Formula Reference
Every essential formula from school algebra to engineering-level differential equations.
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Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Solutions of ax² + bx + c = 0
Difference of Squares
a² − b² = (a+b)(a−b)
Factoring a² − b²
Perfect Square
(a±b)² = a² ± 2ab + b²
Expanding squared binomials
Binomial Cube
(a+b)³ = a³ + 3a²b + 3ab² + b³
Expanding cubed binomials
Sum of Cubes
a³ + b³ = (a+b)(a²−ab+b²)
Factoring sum of cubes
Logarithm Identity
logₐ(xy) = logₐ(x) + logₐ(y)
Product rule for logarithms
Change of Base
logₐ(x) = log(x) / log(a)
Converting between logarithm bases
Exponent Rules
aᵐ · aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ
Basic exponent rules
Arithmetic Series
Sₙ = n/2 · (a₁ + aₙ)
Sum of first n terms of AP
Geometric Series
Sₙ = a₁(1−rⁿ)/(1−r)
Sum of first n terms of GP
Binomial Theorem
(a+b)ⁿ = Σ C(n,k) · aⁿ⁻ᵏ · bᵏ
General expansion of (a+b)ⁿ
79 formulas across 7 categories