Quadratic Formula

For equations of the form ax^2 + bx + c = 0.

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Square of a Sum

(a + b)^2 = a^2 + 2ab + b^2

Square of a Difference

(a - b)^2 = a^2 - 2ab + b^2

Difference of Squares

a^2 - b^2 = (a - b)(a + b)

Cube of a Sum

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Cube of a Difference

(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

Logarithm Definition

\log_a b = c \iff a^c = b

Logarithm of a Product

\log_a(xy) = \log_a x + \log_a y

Logarithm of a Quotient

\log_a(\frac{x}{y}) = \log_a x - \log_a y

Logarithm of a Power

\log_a(x^n) = n \log_a x

Change of Base Formula

\log_a b = \frac{\log_c b}{\log_c a}

Product of Powers

a^m \cdot a^n = a^{m+n}

Quotient of Powers

\frac{a^m}{a^n} = a^{m-n}

Power of a Power

(a^m)^n = a^{m \cdot n}

Product of Roots

\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}

General Form of Complex Number

z = a + bi

Modulus of Complex Number

|z| = \sqrt{a^2 + b^2}

Euler's Formula

e^{ix} = \cos x + i \sin x

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Algebra