SOLUTION: Factor completely and show a detailed solution x^2a + 2x^a y^b + y^2b - 1

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Question 1040173: Factor completely and show a detailed solution
x^2a + 2x^a y^b + y^2b - 1

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Factor completely and show a detailed solution
x^2a + 2x^a y^b + y^2b - 1
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x%5E2a+%2B+2x%5Ea%2Ay%5Eb+%2B+y%5E2b+-+1 = %28x%5Ea+%2B+y%5Eb%29%5E2+-+1 = %28x%5Ea+%2B+y%5Eb+-+1%29%2A%28x%5Ea+%2B+y%5Eb+%2B+1%29.


Completed.

You need to know two facts (two identities):
1) x%5E2+%2B+2xy+%2B+y%5E2 = %28x%2By%29%5E2, and
2) x%5E2+-+1 = %28x%2B1%29%2A%28x-1%29.

Do you know it? If not (or if you are not sure) look into this lesson

    OVERVIEW of shortcut quadratic multiplication formulas

and associated with it.