SOLUTION: Factor Completely 9x^2-16y^2

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Question 248102: Factor Completely 9x^2-16y^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E2-16y%5E2 Start with the given expression.


%283x%29%5E2-16y%5E2 Rewrite 9x%5E2 as %283x%29%5E2.


%283x%29%5E2-%284y%29%5E2 Rewrite 16y%5E2 as %284y%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=3x and B=4y.


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.


%283x%29%5E2-%284y%29%5E2=%283x%2B4y%29%283x-4y%29 Plug in A=3x and B=4y.


So this shows us that 9x%5E2-16y%5E2 factors to %283x%2B4y%29%283x-4y%29.


In other words 9x%5E2-16y%5E2=%283x%2B4y%29%283x-4y%29.