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Factoring the Difference of Two Squares

If you notice that the first term is a perfect square, and the second term is a perfect square, and you have a negative here, we can say that it is "the difference of two squares." What we want to do with this is we want to apply the shortcut that we learned in "factoring trinomials" video 2, to where you take "c" and find factors of that to equal your "b." So what we are going to do is write equivalent statements that mean exactly the same thing. It doesn't change the quantity, it just changes the way it looks a little bit. It's a little bit easier to work with to see our solution coming along. So what I am going to do is put down x squared and plus this place holder, zero x, because obviously there are no x's in, or terms with, just a regular x within this equation. So I have x squared plus zero x minus 16. Notice this is still equivalent to what we started off with. Now applying the shortcut, all we have to do is look for factors of negative 16 that add together to be zero. Those two factors are a positive 4 and a negative 4. Of course, if you add those together, you get zero. So those are our two numbers. Using the shortcut method, all we have to do is put in our two sets of parentheses, and put in our x's in the beginning, and plug in the 4, and the negative 4. And we're done. So you can do this with any of them just as long as know that you do have a perfect square as a first term, a perfect square for the second term, and a negative in between. This only works for the difference of squares, not the sum of squares. That's a whole different ball game minus that's actually prime. I hope this helped in factoring the difference of squares.

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