SOLUTION: Factor the binomial 25x^2-121

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Question 190654: Factor the binomial
25x^2-121
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

25x%5E2-121 Start with the given expression.


%285x%29%5E2-121 Rewrite 25x%5E2 as %285x%29%5E2.


%285x%29%5E2-%2811%29%5E2 Rewrite 121 as %2811%29%5E2.


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


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.


%285x%29%5E2-%2811%29%5E2=%285x%2B11%29%285x-11%29 Plug in A=5x and B=11.


So this shows us that 25x%5E2-121 factors to %285x%2B11%29%285x-11%29.


In other words 25x%5E2-121=%285x%2B11%29%285x-11%29.