SOLUTION: Factor the binomial x^6-y^16

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Question 190661: Factor the binomial
x^6-y^16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E6-y%5E16 Start with the given expression.


%28x%5E3%29%5E2-y%5E16 Rewrite x%5E6 as %28x%5E3%29%5E2.


%28x%5E3%29%5E2-%28y%5E8%29%5E2 Rewrite y%5E16 as %28y%5E8%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=x%5E3 and B=y%5E8.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%28x%5E3%29%5E2-%28y%5E8%29%5E2=%28x%5E3%2By%5E8%29%28x%5E3-y%5E8%29 Plug in A=x%5E3 and B=y%5E8.


So this shows us that x%5E6-y%5E16 factors to %28x%5E3%2By%5E8%29%28x%5E3-y%5E8%29.


In other words x%5E6-y%5E16=%28x%5E3%2By%5E8%29%28x%5E3-y%5E8%29.