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What is the difference of squares formula?

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

What is the perfect square trinomial formula for a^2 + 2ab + b^2?

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

What is the perfect square trinomial formula for a^2 - 2ab + b^2?

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

What is the sum of cubes formula?

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

What is the difference of cubes formula?

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

How do you factor by grouping?

Group like terms: Example: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

What is the quadratic formula?

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

How do you find the vertex of a parabola in standard form?

Use x = \frac{-b}{2a}, then plug in x to get y.

What is the product rule for exponents?

x^a \cdot x^b = x^{a + b}

What is the quotient rule for exponents?

\frac{x^a}{x^b} = x^{a - b}

What is the power rule for exponents?

(x^a)^b = x^{ab}

What does a negative exponent mean?

x^{-a} = \frac{1}{x^a}

What does zero exponent equal?

x^0 = 1, as long as x \neq 0

What does a fractional exponent represent?

x^{a/b} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a

What is the definition of a logarithm?

If b^y = x, then \log_b x = y

What is the product rule for logarithms?

\logb (MN) = \logb M + \log_b N

What is the quotient rule for logarithms?

\logb \left(\frac{M}{N}\right) = \logb M - \log_b N

What is the power rule for logarithms?

\logb (M^p) = p \cdot \logb M

What is the change of base formula?

\logb M = \frac{\logc M}{\log_c b}

How do you solve an equation like |ax + b| = c?

Solve two cases: ax + b = c or ax + b = -c

How do you solve |ax + b| < c?

Convert to compound inequality: -c < ax + b < c

How do you solve |ax + b| > c?

Solve two separate cases: ax + b > c or ax + b < -c

What is the standard form of a complex number?

a + bi

What is i?

i = \sqrt{-1} and i^2 = -1

How do you find the absolute value (modulus) of a complex number?

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