SOLUTION: Factor 64x^2-16

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Question 349504: Factor 64x^2-16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
64x%5E2-16 Start with the given expression.


%288x%29%5E2-16 Rewrite 64x%5E2 as %288x%29%5E2.


%288x%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=8x and B=4.


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.


%288x%29%5E2-%284%29%5E2=%288x%2B4%29%288x-4%29 Plug in A=8x and B=4.


So this shows us that 64x%5E2-16 factors to %288x%2B4%29%288x-4%29.


In other words 64x%5E2-16=%288x%2B4%29%288x-4%29.


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Jim