This video covers the process of FOILing two binomials. Multiply: First, Outer, Inner, Last. A trick is given to help you remember the order.
Welcome to Your Tutor Online video lessons. Today we are going to look at how to FOIL. FOILing is what you do when you multiply two binominals together. FOIL is an acronym which stands for First, Outer, Inner, and Last.
When we talk about the first terms, we are going to look at each respective parenthesis. The first term in each parenthesis is the first term. The outer terms are for the outside of the entire thing, our 2x and our negative 5 are both our outside terms. The inside is just the opposite, so the two closest to each other. And then last, the two terms that are last in each of the parenthesis. So, 3 and negative 5.
And now we just follow our acronym in order: First, Outer, Inner, Last. First, we will multipy together our two first terms, our 2x and our x which gives us 2x squared. Next is outer, 2x and negative 5. 2x times negative 5 is negative 10x. Our inside terms are 3 and x which gives us positive 3x. And our last terms 3 and negative 5 gives us negative 15.
Now, almost always you will end up with your two middle terms being like terms so you just want to combine those two as your final answer. 2x squared, combine our two like terms (-10x and positve 3x) gives us negative 7x and minus 15.
Here’s a tip for you to remember to do the FOILing in the correct way. If you look back up here, how I drew the lines, I have almost a little smile face. Here is the smile, the nose, and two eye-ball looking things. If you get the smile face at the end that means you drew your FOIL correctly and you multiplied the terms together correctly.
Alright, I am going to show you how to draw this face one more time so you have a good check for when you have to do FOIL on your own. We are going to follow in order: First, Outer, Inside, Last. For the first term, we will start above the problem. Connect the first two terms with an arc. So in this example, 3x and 2x and that will give us our first eye brow. Now the outside, we will connect our two outside terms 3x and 1, which gives us our smile. The inside terms, the 2 and the 2x, gives us our nose. And our last terms, negative 2 and positive 1, give us our last eyebrow. And now if you did it correctly you will see a face in here. And now you know you did your problem correctly.
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