Factorize the following:

The greatest common factor of the terms $10 m^{3} n^{2}, 15 m^{4} n$ and $-20 m^{2} n^{3}$ of the expression $10 m^{3} n^{2}+15 m^{4} n-20 m^{2} n^{3}$ is $5 m^{2} n$.

Now,

$10 m^{3} n^{2}=5 m^{2} n \times 2 m n$

$15 m^{4} n=5 m^{2} n \times 3 m^{2}$

$-20 m^{2} n^{3}=5 m^{2} n \times-4 n^{2}$

Hence, 10m3n2 + 15m2n - 20m2n3 ​can be factorised as 5m2n(2mn + 3m2 - 4n2).​