SOLUTION: Use the “difference of squares” rule to factor the following expression: 36x^2-9y^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the “difference of squares” rule to factor the following expression: 36x^2-9y^2       Log On


   

Question 385275: Use the “difference of squares” rule to factor the following expression:
36x^2-9y^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

36x%5E2-9y%5E2 Start with the given expression.


%286x%29%5E2-9y%5E2 Rewrite 36x%5E2 as %286x%29%5E2.


%286x%29%5E2-%283y%29%5E2 Rewrite 9y%5E2 as %283y%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=6x and B=3y.


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.


%286x%29%5E2-%283y%29%5E2=%286x%2B3y%29%286x-3y%29 Plug in A=6x and B=3y.


So this shows us that 36x%5E2-9y%5E2 factors to %286x%2B3y%29%286x-3y%29.


In other words 36x%5E2-9y%5E2=%286x%2B3y%29%286x-3y%29.


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Jim