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Basic Algebra Formulas

Here you'll find all of your basic algebra formulas for the following topics:




Laws of Exponents


There are several different "laws" or properties when working with exponents:

basic algebra formulas

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.

FOIL Method

For detailed examples on using the FOIL Method, please click here.





Square of a Binomial


To 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:

square of a binomial

Click here for step by step examples on squaring a binomial.






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:

difference of two squares

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 backwords 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.

perfect square trinomial



Difference of Two Squares

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:

Difference of Two Cubes



Quadratic Formula


There are two formulas that are associated with quadratic equations: the vertex formula and the quadratic formula.


Vertex Formula

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

vertex formula

Click here for detailed examples on using the vertex formula.



Quadratic Formula

You can use the quadratic formula to solve ANY quadratic equation. It is used most when the quadratic equation is non-factorable.

quadratic formula

Click here to see step-by-step examples using the quadratic formula.



Our last basic algebra formula is the Pythagorean Theorem.



Pythagorean Theorem


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

pythagorean theorem

Click here for detailed examples on using the Pythagorean Theorem.



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