04-3c+Binomials+and+Trinomials

Quadratic equations can have one, two or three terms. The only restriction is that the equation must have a squared term to be considered a quadratic equation.

A quadratic expression with one term is a **//monomial.//** A quadratic expression with two terms is a //**binomial**// A quadratic expression with three terms is a //**trinomial**//.

Certain quadratic expressions that contain perfect squares have special factoring rules. If you notice that a quadratic expression follows one of the special patterns, you can immediately factor it without going through the normal trial and error process. The first special pattern is the difference of two squares. In this pattern, which is a binomial version of a quadratic expression, both terms are perfect squares, and one is subtracted from the other.

The difference of two squares is factored like this: a 2 - b 2 = (a + b) (a - b)

//**This pattern only works for the DIFFERENCE of two squares; it does not hold for the SUM of two squares.**//

The second special factoring pattern occurs when the expression is a Perfect Square Trinomial. These trinomials take one of two forms:

a 2 + 2ab + b 2 or a 2 - 2ab + b 2 In the case when the sign of the middle term is positive, the factoring pattern is a 2 + 2ab + b 2 = (a + b) 2 while in the case of a negative middle term, the factoring pattern is a 2 - 2ab + b 2 = (a - b) 2 And you were wondering why you needed to memorize all those perfect squares! Half the battle is spotting the patterns! You can still factor one of the special patterns using your regular factoring skills, but the patterns will save you a lot of time! Proceed to Modeling the Flight of a Ball