Factorize the following:
Question:

Factorize the following:
2l2mn – 3lm2n + 4lmn2

Solution:

The greatest common factor of the terms $2 l^{2} m n, 3 l m^{2} n$ and $4 l m n^{2}$ of the expression $2 l^{2} m n-3 l m^{2} n+4 l m n^{2}$ is lmn.

Also, we can write $2 l^{2} m n=l m n \times 2 l, 3 l m^{2} n=l m n \times 3 m$ and $4 l m n^{2}=l m n \times 4 n .$

$\therefore 2 l^{2} n m-3 l m^{2} n+4 l m n^{2}=l m n \times 2 l-l m n \times 3 m+l m n \times 4 n$

$=\operatorname{lm} n(2 l-3 m+4 n)$