Quadratic Formula
x = (-b ± √(b²-4ac)) / 2a
Solves ax² + bx + c = 0
Difference of Squares
a² - b² = (a+b)(a-b)
Factoring shortcut
Perfect Square Trinomial
(a+b)² = a² + 2ab + b²
Expanding squared binomial
Sum of Cubes
a³ + b³ = (a+b)(a²-ab+b²)
Factoring sum of cubes
Difference of Cubes
a³ - b³ = (a-b)(a²+ab+b²)
Factoring difference of cubes
Binomial Theorem
(a+b)ⁿ = Σ C(n,k) aⁿ⁻ᵏ bᵏ
Expanding a binomial raised to power n
Slope Formula
m = (y₂-y₁)/(x₂-x₁)
Slope between two points
Slope-Intercept
y = mx + b
Linear equation form
Distance Formula
d = √((x₂-x₁)² + (y₂-y₁)²)
Distance between two points
Midpoint Formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Midpoint between two points
Exponent Product
aᵐ × aⁿ = aᵐ⁺ⁿ
Multiplying same base
Exponent Quotient
aᵐ / aⁿ = aᵐ⁻ⁿ
Dividing same base