Multiply each term of $ \left( \color{blue}{n-1}\right) $ by each term in $ \left( n -\cancel{1}+ \cancel{1}\right) $.

$$ \left( \color{blue}{n-1}\right) \cdot \left( n -\cancel{1}+ \cancel{1}\right) = \\ = n^2 -\cancel{n}+ \cancel{n} -\cancel{n}+ \cancel{1} -\cancel{1} $$

Combine like terms:

$$ n^2 \, \color{blue}{ -\cancel{n}} \,+ \, \color{green}{ \cancel{n}} \, \, \color{green}{ -\cancel{n}} \,+ \, \color{blue}{ \cancel{1}} \, \, \color{blue}{ -\cancel{1}} \, = n^2 \color{green}{-n} $$

Multiply $m^2$ by $ \dfrac{n^2-n}{2} $ to get $ \dfrac{ m^2n^2-m^2n }{ 2 } $.

Step 1: Write $ m^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} m^2 \cdot \frac{n^2-n}{2} & \xlongequal{\text{Step 1}} \frac{m^2}{\color{red}{1}} \cdot \frac{n^2-n}{2} \xlongequal{\text{Step 2}} \frac{ m^2 \cdot \left( n^2-n \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ m^2n^2-m^2n }{ 2 } \end{aligned} $$

Add $n$ and $ \dfrac{m^2n^2-m^2n}{2} $ to get $ \dfrac{ \color{purple}{ m^2n^2-m^2n+2n } }{ 2 }$.

Step 1: Write $ n $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} n+ \frac{m^2n^2-m^2n}{2} & \xlongequal{\text{Step 1}} \frac{n}{\color{red}{1}} + \frac{m^2n^2-m^2n}{2} = \frac{ n \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ m^2n^2-m^2n }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2n } }{ 2 } + \frac{ \color{purple}{ m^2n^2-m^2n } }{ 2 }=\frac{ \color{purple}{ m^2n^2-m^2n+2n } }{ 2 } \end{aligned} $$