Find a value for k so the 9m^2-kn^2 will have the factors 3m + 7n and 3m -7n. Please show me how to get this and show the work please.
Use that (a-b)(a+b) = a^2 - b^2
So, you can read-off that k = 49.
To find the value of k that will make the expression 9m^2 - kn^2 have the factors 3m + 7n and 3m - 7n, we can use the property of the difference of squares.
The property states that (a - b)(a + b) = a^2 - b^2.
In this case, we need to factor out the expression 9m^2 - kn^2 using the given factors: 3m + 7n and 3m - 7n.
Let's assume that the factors are correct, so we can write the equation as:
(3m + 7n)(3m - 7n) = 9m^2 - kn^2.
To find the value of k, we will use the property of the difference of squares in reverse.
Comparing the equation to the difference of squares property, we can see that a^2 is 9m^2 and b^2 is kn^2.
So, we have:
(3m + 7n)(3m - 7n) = (3m)^2 - (7n)^2.
Simplifying further, we get:
9m^2 - 49n^2 = 9m^2 - kn^2.
Now, comparing the two equations:
9m^2 - 49n^2 = 9m^2 - kn^2,
we can see that the values of a^2 and b^2 are the same. This means that k must equal 49 in order for the equation to hold true.
Therefore, the value of k that will make the expression 9m^2 - kn^2 have the factors 3m + 7n and 3m - 7n is k = 49.