SOLUTION: Factor the binomial 25x^2-1

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Question 190652: Factor the binomial
25x^2-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

25x%5E2-1 Start with the given expression.


%285x%29%5E2-1 Rewrite 25x%5E2 as %285x%29%5E2.


%285x%29%5E2-%281%29%5E2 Rewrite 1 as %281%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=5x and B=1.


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.


%285x%29%5E2-%281%29%5E2=%285x%2B1%29%285x-1%29 Plug in A=5x and B=1.


So this shows us that 25x%5E2-1 factors to %285x%2B1%29%285x-1%29.


In other words 25x%5E2-1=%285x%2B1%29%285x-1%29.