Multiplying Binomials using the foil method.

A binomial is a polynomial with two terms.

The FOIL method stands for,
F = First
O = Outer
I = Inner
L = Last

This video works three example problems in which the answer is a "difference of two squares".

Instead of being the same sign the binomials will have an opposite sign. You will have a +4 x -4. Let's foil this out. First times first which equals x^2. Next is outer, x x 4 = 4 x,inner - 4 x -4x = -4x, and last 4 x -4 = -16. What do you notice about these terms? We had one of these in the last lesson.The signs are opposite so they cancel each other out, because 4x-4x cancel each other out. What we have left is x^2 and back here we have -16. This is called the difference of two squares. x^2 is a perfect square, and 16 is a perfect square, and difference means subtraction, so when you multiply these together you will end up with a binomial answer. Let's look at 2x -5 and 2x + 5, and see what happens with it? (or is it a z?)
(2z - 5) (2z + 5) First 2z x 2z = 4 z, outer 10Z x , inner is -10z, and last is -25. Be very careful with the sign, bring down a 4z^2 and -25, and that is the product of a difference of squares.
Now let's look at number 6. (4r +7y)(4r-7y)
I will write out the answer and see if you can get it.
Does the order matter? The order of product doesn't matter because think of 3 x 4 , and 4 x 3, you will get the same product so it doesn't matter. First, outer, inner, and last From there I can cross the middel terms out, and I get 16r^2 - 49y^2. There you go.

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