SOLUTION: factor 16-4x^2

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Question 190756: factor
16-4x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

16-4x%5E2 Start with the given expression.


%284%29%5E2-4x%5E2 Rewrite 16 as %284%29%5E2.


%284%29%5E2-%282x%29%5E2 Rewrite 4x%5E2 as %282x%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=4 and B=2x.


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.


%284%29%5E2-%282x%29%5E2=%284%2B2x%29%284-2x%29 Plug in A=4 and B=2x.


So this shows us that 16-4x%5E2 factors to %284%2B2x%29%284-2x%29.


In other words 16-4x%5E2=%284%2B2x%29%284-2x%29.