SOLUTION: Factor: 16x²-81

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Question 196925: Factor: 16x²-81
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

16x%5E2-81 Start with the given expression.


%284x%29%5E2-81 Rewrite 16x%5E2 as %284x%29%5E2.


%284x%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=4x 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.


%284x%29%5E2-%289%29%5E2=%284x%2B9%29%284x-9%29 Plug in A=4x and B=9.


So this shows us that 16x%5E2-81 factors to %284x%2B9%29%284x-9%29.


In other words 16x%5E2-81=%284x%2B9%29%284x-9%29.