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Math 10 – FOIL Method: Multiplying Two Binomials

One of the things I learned in Math 10 this week is multiplying two binomials. There are a lot of methods to use but the most efficient method is FOIL Method; or First, Outer, Inner, Last.

To do the FOIL method, first, find out if you’re multiplying a polynomial with two terms each. E.g.

screenshot_5  So now, we have two binomials that we can multiply. (x + 2)(x + 3y)

How does the FOIL method works? First, you need to know what terms are First, Outer, Inner, and Last.

So, how do you determine which is which? The first terms are obviously the first terms in each polynomial. In our example it is x and x. The outer terms are the terms ‘outside’ or the ones in both ends of your equation/expression. In our given example, they are the terms x and 3y. The inner terms are the terms ‘inside’ or the two terms in the center of your equation. In our example, they are 2 and x. Lastly, the last terms are the the second terms in each polynomial. It’s 2 and 3y in the example given.

Note: You CANNOT multiply the terms inside of the bracket as they are divided by either addition or subtraction depending on your polynomials.

Continuing the example, (x + 2)(x + 3y), now we need to multiply the binomials. Remember, FOIL

screenshot_2

{x}\cdot{x}=x^2

screenshot_3

{x}\cdot{3y}=3xy

screenshot_4

{2}\cdot{x}=2x

screenshot_6

{2}\cdot{3y}=6y

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