SOLUTION: Factor completely and show steps: 4x^2-36y^2

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Question 181870: Factor completely and show steps:
4x^2-36y^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-36y%5E2 Start with the given expression.


%282x%29%5E2-36y%5E2 Rewrite 4x%5E2 as %282x%29%5E2.


%282x%29%5E2-%286y%29%5E2 Rewrite 36y%5E2 as %286y%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=2x and B=6y.


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.


%282x%29%5E2-%286y%29%5E2=%282x%2B6y%29%282x-6y%29 Plug in A=2x and B=6y.


So this shows us that 4x%5E2-36y%5E2 factors to %282x%2B6y%29%282x-6y%29.


In other words 4x%5E2-36y%5E2=%282x%2B6y%29%282x-6y%29.