Factor m^2-k^2+6k-9
^2 means squared. The answer is
(m-k+3)(m+k-3)
I want to know how to get that. Thanks.
Look at this:
m^2 - (k^2 -6k + 9)
m^2 - (k -3)^2
Now that is the difference of two squares...
Thanks!!
To factor the expression m^2 - k^2 + 6k - 9, you can start by grouping the terms. Notice that the first two terms, m^2 and -k^2, form a difference of squares pattern since it is in the form a^2 - b^2. This can be factored as (a - b)(a + b), where a = m and b = k.
So, m^2 - k^2 can be factored as (m - k)(m + k).
Next, look at the remaining terms, 6k - 9. Notice that both terms have a common factor of 3. So, you can rewrite this as 3(2k - 3).
Now, you can combine the factored terms: (m - k)(m + k) + 3(2k - 3).
To simplify further, distribute the factor of 3: (m - k)(m + k) + 6k - 9.
Now, you can combine the like terms: (m - k)(m + k + 6) - 9.
Finally, notice that the expression m + k + 6 is equal to m + k + (-3) + 9. Rearranging the terms, you get (m + k - 3) + 9.
Combining all the factors, you get (m - k)(m + k - 3) + 9, or equivalently, (m - k)(m + k - 3) + 3^2.
Therefore, the fully factored form of m^2 - k^2 + 6k - 9 is (m - k)(m + k - 3) + 3^2, which can be written as (m - k + 3)(m + k - 3).