Math CentralQuandaries & Queries


Question from Shell, a student:

complete Factor: x^2-y^2


There is a great deal of pattern recognition in factoring, by that I mean looking at an expression and seeing patterns you have seen before and recognizing how to factor them. This is true of the "difference of squares" you sent us, x2 - y2. Once you think you know the factors you can check by multiplication. Here are three possibilities for factorizations of x2 - y2.

(x + y)(x + y)
(x + y)(x - y)
(x - y)(x - y)

Expand each of them and see which simplifies to x2 - y2.


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