Algebra Formulas

Quadratic Formula

x = (−b ± √(b²−4ac)) / 2a

For ax² + bx + c = 0

Example x = 2, 3

Slope of a Line

m = (y₂ − y₁)/(x₂ − x₁)

Rise over run

Example m = 3

Slope–Intercept Form

y = mx + b

m = slope, b = y-intercept

Example y = 7

Product of Powers

aᵐ × aⁿ = aᵐ⁺ⁿ

Same base: add exponents

Example 128

Power of a Power

(aᵐ)ⁿ = aᵐⁿ

Multiply exponents

Example 729

Difference of Squares

a² − b² = (a−b)(a+b)

Factor difference of squares

Example 16

Perfect Square Trinomial

(a+b)² = a² + 2ab + b²

Square of a sum

Example x² + 6x + 9

Distance Between Points

d = √[(x₂−x₁)² + (y₂−y₁)²]

Coordinate distance

Example d = 5

Midpoint Formula

M = ((x₁+x₂)/2, (y₁+y₂)/2)

Average of coordinates

Example (4, 7)

Quotient of Powers

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

Same base: subtract exponents

Example 625

Zero Exponent

a⁰ = 1

Any non-zero number to the power 0 is 1

Example 1

FOIL (Binomials)

(a+b)(c+d) = ac + ad + bc + bd

First, Outer, Inner, Last

Example x² + 5x + 6

Arithmetic Sequence nth Term

aₙ = a₁ + (n−1)d

Common difference d between terms

Example 19

Geometric Sequence nth Term

aₙ = a₁ × rⁿ⁻¹

Common ratio r between terms

Example 54