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.
[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.
