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.

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.