# Basic Algebra Formulas

## Laws of Exponents

There are several different "laws" or properties when working with exponents: For detailed examples on how to use the laws of exponents, click here.

Next we'll look at a few formulas that can be used when working with polynomials.

## Polynomial Formulas

There are special rules or formulas that can be used when multiplying polynomials or factoring polynomials. Let's take a look:

## Multiplying Polynomials Using FOIL

To multiply two polynomials, multiply each term in the first polynomial by each term in the second polynomial. This is also known as using FOIL. ## Square of a Binomial

o square a binomial, you add: the square of the first term, twice the product of the two terms, and the square of the last term. Take a look: ## Difference of Two Squares

When two binomials differ only by the sign between their terms (one a plus, the other a minus), we call this a Difference of Two Squares.

The rule is very easy to remember: Subtract the square of the second term from the square of the first term. Take a look: Step by step examples of problems involving a difference of two squares can be found here.

## Polynomials - Special Factoring

The following formulas will actually take our special products from above and work backwards to factor. Same rules, we are just working backwards to find the factors.

## Perfect Square Trinomial

A perfect square trinomial results in binomial squares.

If you notice that the first and last terms are perfect squares, then check to see if the trinomial factors as a binomial square. ## Difference of Two Squares ## The Sum and Difference of Two Cubes

The following are the formulas for factoring the sum and difference of two cubes: ou can use the quadratic formula to solve ANY quadratic equation. It is used most when the quadratic equation is non-factorable. ## Vertex Formula

The vertex formula is used when you must find the vertex (minimum or maximum point) of the parabola. ## Pythagorean Theorem

The Pythagorean Theorem is used to identify the length of the sides of any right triangle. 