Mathway | Algebra Formulas

Exponents

$a^{0} = 1, a \neq 0 (a^{n})^{m} = a^{n m} (a b)^{n} = a^{n} b^{n} a^{n} a^{m} = a^{n + m} a^{- n} = \frac{1}{a^{n}} \frac{1}{a^{- n}} = a^{n} a^{n} + a^{m} = a^{n + m} \frac{a^{n}}{a^{m}} = a^{m - n} {(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}} {(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n} = \frac{b^{n}}{a^{n}}$

Absolute Value

$|- a| = a |- a| = |a| |a| = a, a = 0 |a x| = a |x|, a = 0$

Factoring

$x^{2} - y^{2} = (x - y) (x + y) x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2}) x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$

Pythagorean Theorem

$a^{2} + b^{2} = c^{2}$

Linear Equations

$Point-Slope Form: y - y_{1} = m (x - x_{1}) Standard Form: A x + B y = C Slope-Intercept Form: y = m x + b$

Quadratic Formula

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

Distance Formula

$Given Points A (x_{1}, y_{1}) and B (x_{2}, y_{2}) A B = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$

Midpoint Formula

$Midpoint of A B = (\frac{x_{2} + x_{1}}{2}, \frac{y_{2} + y_{1}}{2})$

Slope of a line through two points

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$