SOLUTION: Factor the binomial 121x^2-100y^2

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Question 190655: Factor the binomial
121x^2-100y^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

121x%5E2-100y%5E2 Start with the given expression.


%2811x%29%5E2-100y%5E2 Rewrite 121x%5E2 as %2811x%29%5E2.


%2811x%29%5E2-%2810y%29%5E2 Rewrite 100y%5E2 as %2810y%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=11x and B=10y.


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.


%2811x%29%5E2-%2810y%29%5E2=%2811x%2B10y%29%2811x-10y%29 Plug in A=11x and B=10y.


So this shows us that 121x%5E2-100y%5E2 factors to %2811x%2B10y%29%2811x-10y%29.


In other words 121x%5E2-100y%5E2=%2811x%2B10y%29%2811x-10y%29.