Algebra Formulas

Square of Sum

(a + b)² = a² + 2ab + b²

Useful for expanding binomials and simplifying expressions.

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Square of Difference

(a - b)² = a² - 2ab + b²

Similar to the square of a sum, but for subtraction.

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Difference of Squares

a² - b² = (a+b)(a-b)

A fundamental factoring identity.

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Quadratic Formula

x = [-b ± √(b² - 4ac)] / 2a

Solves for the roots of any quadratic equation.

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Linear Equation

y = mx + b

Represents a straight line on a coordinate plane.

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Function Composition

(f ∘ g)(x) = f(g(x))

Applies one function to the result of another.

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Inverse Function

f(f⁻¹(x)) = x

Reverses the effect of a function.

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Arithmetic Sequence

aₙ = a₁ + (n-1)d

Defines a sequence with a constant difference between terms.

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Geometric Sequence

aₙ = a₁rⁿ⁻¹

Defines a sequence with a constant ratio between terms.

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Laws of Exponents

xᵃ · xᵇ = xᵃ⁺ᵇ

Rules for manipulating exponents in algebraic expressions.

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Logarithm Rules

log(xy) = log(x) + log(y)

Rules for simplifying logarithmic expressions.

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Cubic Formula

(a + b)³ = a³ + 3a²b + 3ab² + b³

Expansion of a cubic binomial.

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Factor Theorem

If f(a) = 0, then (x-a) is a factor of f(x)

Determines if a binomial is a factor of a polynomial.

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