SOLUTION: Factor the binomial -81+x^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the binomial -81+x^2      Log On


   

Question 190658: Factor the binomial
-81+x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-81%2Bx%5E2 Start with the given expression.


x%5E2-81 Rearrange the terms.


%28x%29%5E2-81 Rewrite x%5E2 as %28x%29%5E2.


%28x%29%5E2-%289%29%5E2 Rewrite 81 as %289%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=x and B=9.


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.


%28x%29%5E2-%289%29%5E2=%28x%2B9%29%28x-9%29 Plug in A=x and B=9.


So this shows us that -81%2Bx%5E2 factors to %28x%2B9%29%28x-9%29.


In other words -81%2Bx%5E2=%28x%2B9%29%28x-9%29.