SOLUTION: Factor the binomial x^2-49

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Question 190662: Factor the binomial
x^2-49
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-49 Start with the given expression.


%28x%29%5E2-49 Rewrite x%5E2 as %28x%29%5E2.


%28x%29%5E2-%287%29%5E2 Rewrite 49 as %287%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=x and B=7.


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.


%28x%29%5E2-%287%29%5E2=%28x%2B7%29%28x-7%29 Plug in A=x and B=7.


So this shows us that x%5E2-49 factors to %28x%2B7%29%28x-7%29.


In other words x%5E2-49=%28x%2B7%29%28x-7%29.