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Algebra Help: Simplify Equations Using the FOIL Method

You probably already know how to simplify an equation like 6(2x-3). Using the distributive property, you multiply 6*2x and then 6*(-3) to get 12x-18. What about an equation like (2x+4)*(3x-5)? For these kinds of equations, you need to use the FOIL method. FOIL stands for First, Outside, Inside, Last, and is a simple way to keep track of how to multiply equations with two binomials. This article will explain how to use it with an example.


Let's take the example we gave in the introduction. (2x+4)*(3x-5)=


The first step in FOIL is to multiply the first element in the first set of parentheses by the first element in the second set of parentheses. In our example, 2x*3x=6x^2.


Next, multiply the two terms on the outside of the equation, in this case, 2x*-5=-10x.


Now multiply the terms on the inside of the equation, 4*3x=12x.


Find the product of the last terms in both parentheses. 4*-5=-20.

Combine and Simplify

Finally, put it all together. We have 6x^2-10x+12x-20, which we simplify to 6x^2+2x-20.

Complicate It

The FOIL method really only works on equations with two binomials. If you have an equation with more then two, say (x+3)(3x-4)(-2x+8), then run FOIL on two of the binomials then use the distributive property on the remaining binomial.

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