SOLUTION: Factor the binomial -9r^2+1

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Question 190657: Factor the binomial
-9r^2+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-9r%5E2%2B1 Start with the given expression.


1-9r%5E2 Rearrange the terms


%281%29%5E2-9r%5E2 Rewrite 1 as %281%29%5E2.


%281%29%5E2-%283r%29%5E2 Rewrite 9r%5E2 as %283r%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=1 and B=3r.


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.


%281%29%5E2-%283r%29%5E2=%281%2B3r%29%281-3r%29 Plug in A=1 and B=3r.


So this shows us that -9r%5E2%2B1 factors to %281%2B3r%29%281-3r%29.


In other words -9r%5E2%2B1=%281%2B3r%29%281-3r%29.