factor out the greatest common factor -36m^2n^3-60mn^4+18m^4n^2
6mn^2(6mn - 10n^2 + 3m^3)
To factor out the greatest common factor from the given expression -36m^2n^3 - 60mn^4 + 18m^4n^2, we first need to identify the common factors among the terms.
In this case, the common factor is the greatest power of each variable that appears in every term. In this expression, we have m^2, m, n^3, n^4, m^4, and n^2. The greatest power of m that appears in every term is m^2, the greatest power of n is n^3, and the greatest power of m^4n^2 is m^4n^2.
So we have identified the greatest common factor as m^2n^3.
To factor out the greatest common factor, we divide each term by this factor. Here's how:
-36m^2n^3 / (m^2n^3) = -36
-60mn^4 / (m^2n^3) = -60n
18m^4n^2 / (m^2n^3) = 18m^2
Putting it all together, we can factor out the greatest common factor -36m^2n^3 as follows:
-36m^2n^3 - 60mn^4 + 18m^4n^2 = m^2n^3(-36 - 60n + 18m^2)