SOLUTION: Factor the binomial x^2y^2-4

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Question 190656: Factor the binomial
x^2y^2-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2y%5E2-4 Start with the given expression.


%28xy%29%5E2-4 Rewrite x%5E2y%5E2 as %28xy%29%5E2.


%28xy%29%5E2-%282%29%5E2 Rewrite 4 as %282%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=xy and B=2.


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.


%28xy%29%5E2-%282%29%5E2=%28xy%2B2%29%28xy-2%29 Plug in A=xy and B=2.


So this shows us that x%5E2y%5E2-4 factors to %28xy%2B2%29%28xy-2%29.


In other words x%5E2y%5E2-4=%28xy%2B2%29%28xy-2%29.