Simplify [tex]-3mn + m^2n + 3mn - mn^2 + 2m - m[/tex].

A. [tex]m + 2[/tex]

B. [tex]m[/tex]

C. [tex]m^2n - mn^2 + m[/tex]

D. [tex]m^2n - mn^2 + mn + 2[/tex]



Answer :

Let's look at the expression we need to simplify step by step. The given expression is:

[tex]\[ -3mn + m^2n + 3mn - mn^2 + 2m - m \][/tex]

First, let's combine all the like terms in the expression:

1. Combine the terms involving \( mn \):

[tex]\[ -3mn + 3mn = 0 \][/tex]

This means these terms cancel each other out.

2. Now, let's look at the remaining expression after combining the \( mn \) terms:

[tex]\[ m^2n - mn^2 + 2m - m \][/tex]

3. Combine the terms involving \( m \):

[tex]\[ 2m - m = m \][/tex]

Now, we have:

[tex]\[ m^2n - mn^2 + m \][/tex]

This is the simplified form of the given expression. Hence, we can factor this expression further by pulling out common factors:

Notice that \( m \) is a common factor in all terms:

[tex]\[ m(mn - n^2 + 1) \][/tex]

Therefore, the final simplified expression is:

[tex]\[ m(mn - n^2 + 1) \][/tex]

This is the simplified form of the given expression.