m^2-3mn-28n^2

To factor the expression \(m^2 - 3mn - 28n^2\), we need to find two numbers that multiply to the coefficient of \(m^2\) (1) and add up to the coefficient of the middle term (-3).

The two numbers that meet these requirements are -7 and 4, because -7 * 4 = -28 and -7 + 4 = -3.

So, we can rewrite the expression as:

\(m^2 - 7mn + 4mn - 28n^2\)

Now, we can factor by grouping:

\(m(m - 7n) + 4n(m - 7n)\)

Finally, we can factor out the common factor of \(m - 7n\) to get:

\((m + 4n)(m - 7n)\)

Therefore, \(m^2 - 3mn - 28n^2\) factors to \((m + 4n)(m - 7n)\).