# 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

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

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

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