Algebra Formulas

A List of Common Algebra Formulas

Here are some of the most commonly used formulas in algebra. If you have one you'd like to be added, or find an error, please contact me.

Laws of Exponents

  • \(a^ma^n=a^{m+n}\)
  • \((a*b)^m=a^mb^m\)
  • \((a^m)^n=a^{mn}\)
  • \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\)
  • \(a^0=1\)
  • \(\frac{a^m}{a^n}=a^{m-n}\)
  • \(a^{-m}=\frac{1}{a^m}\)

Quadratic Formula

For an equation of the form \(ax^2+bx+c=0\), you can solve for x using the Quadratic Formula:

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

Binomial Theorem

  • \((a+b)^1= a + b\)
  • \((a+b)^2=a^2+2ab+b^2\)
  • \((a+b)^3=a^3+3a^2b+3ab^2+b^3\)
  • \((a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)

Difference of Squares

  • \(a^2-b^2=(a-b)(a+b)\)

Rules of Zero

  • \(\frac{0}{x} = 0\text{, where }x \neq 0.\)
  • \(a^0=1\)
  • \(0^a=0\)
  • \(a*0 = 0\)
  • \(\frac{a}{0}\text{ is undefined (you can't do it)}\)