Key Information

First Step - Multiplying Binomials

Key Information Topic B:

Using Factoring
First Step - Multiplying Binomials
Factoring a Quadratic

In order to break down a quadratic into two binomials, you need to factor the quadratic. Factoring can be a difficult task for students and a difficult concept to teach. Teachers should start by teaching the multiplication of binomials.

In the following example, the distributive method is used to multiply two binomials to create a quadratic equation.

(x+2)(x-3)

Multiply the first term in the first binomial times both terms in the second binomial x(x-3)	Multiply the second term in the first binomial times both terms in the second binomial 2(x-3)
x(x) + x(-3)	+2(x)-2(-3)
Combine terms above x²-3x+2x-6
Combine the like terms so you get… x²-x-6

Note, the product of two binomial in this case is a trinomial (a expression with three terms).

This method is also known as FOIL (First Outside Inside Last). Teachers should teach the use of the distributive method to multiply binomials prior to introducing FOIL, because FOIL is simply the acronym for using the distributive property. Often, students mistake the acronym for the method. In other words, they memorize how to use FOIL, but they do not understand that they are using the distributive property. They go through the mechanics of the problem without understanding the reasoning behind using the distributive property.