In Exercises 39–48, factor the difference of two squares. x^2−144

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Hello. Today, we're going to be factoring a given expression. So the expression given to us is X squared minus 169. Now, if you take a look at the first term and the last term, both of these terms are perfect squares, x squared could be rewritten as X raised to the power of two and 169 can be rewritten as 13 squared. So what we have here is a difference of square terms and we have a special Factory Ization for that. If we have a quantity A squared minus B squared, this could be rewritten or factored to a plus B times a minus B. So in order to use this factory Ization, we need to go ahead and identify what are A and B are going to be. Well, A is just gonna be the factor of the first term. So A is going to equal to X. And B is going to be a factor of the second term. So B is equal to 13. Now, all we need to do is go ahead and plug it into our factory ization in order to factor this difference of squares. So doing so is going to give me a plus B or X plus 13 times a minus B or x minus 13. And this is going to be the complete factory ization of our difference of squares. And that means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to factor a difference of squares and I'll go ahead and see you all in the next video.

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