Question 83422
If you want factors of 3m+7n and 3m-7n  simply set up the factorization like this:


{{{(3m+7n)(3m-7n)}}}


Now foil


{{{9m^2+21mn-21mn-49n^2=9m^2-49n^2}}}


Now set the expression {{{9m ^2 - kn^2}}} equal to {{{9m^2-49n^2}}} to solve for k


{{{9m^2-49n^2=9m ^2 - kn^2}}} 


{{{-49n^2=- kn^2}}} Subtract {{{9m^2}}} from both sides


{{{-49=- k}}} Divide both sides by {{{n^2}}}


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


{{{k=49}}}