SOLUTION: Find a value for k so that 9m ^2 - kn^2 will have the factors 3m+7n and 3m-7n

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Question 83422: Find a value for k so that 9m ^2 - kn^2 will have the factors 3m+7n and 3m-7n
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you want factors of 3m+7n and 3m-7n simply set up the factorization like this:

%283m%2B7n%29%283m-7n%29

Now foil

9m%5E2%2B21mn-21mn-49n%5E2=9m%5E2-49n%5E2

Now set the expression 9m+%5E2+-+kn%5E2 equal to 9m%5E2-49n%5E2 to solve for k

9m%5E2-49n%5E2=9m+%5E2+-+kn%5E2

-49n%5E2=-+kn%5E2 Subtract 9m%5E2 from both sides

-49=-+k Divide both sides by n%5E2

49=+k Multiply both sides by -1 to make k positive. So k comes to be

k=49