SOLUTION: Please help this is confusing to me. Find a value for k so tha 9m^2 - kn^2 will have the factors 3m + 7n and 3m - 7n.

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Question 77222: Please help this is confusing to me.
Find a value for k so tha 9m^2 - kn^2 will have the factors 3m + 7n and 3m - 7n.
Found 2 solutions by THANApHD, jim_thompson5910:
Answer by THANApHD(104) About Me  (Show Source):
You can put this solution on YOUR website!
9m^2 - kn^2 can be written in factor form as like this
9m^2 - kn^2 = (3m+7n)(3m-7n)
9m^2 - kn^2 = 9m^2 - 49n^2
so
kn^2 = 49n^2
k =49

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you foil %283m+%2B+7n%29%283m+-+7n%29 you get
%283m+%2B+7n%29%283m+-+7n%29=9m%5E2%2B21mn-21mn-49n%5E2
%283m+%2B+7n%29%283m+-+7n%29=9m%5E2%2Bcross%2821mn-21mn%29-49n%5E2 Notice the middle terms cancel
%283m+%2B+7n%29%283m+-+7n%29=9m%5E2-49n%5E2
So we have 9m%5E2-49n%5E2 which is equal to 9m%5E2+-+kn%5E2 so in other words:
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 Divide both sides by -1
So we get
k=49