Multiply $75$ by $ \dfrac{x^2}{50} $ to get $ \dfrac{ 75x^2 }{ 50 } $.

Step 1: Write $ 75 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 75 \cdot \frac{x^2}{50} & \xlongequal{\text{Step 1}} \frac{75}{\color{red}{1}} \cdot \frac{x^2}{50} \xlongequal{\text{Step 2}} \frac{ 75 \cdot x^2 }{ 1 \cdot 50 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 75x^2 }{ 50 } \end{aligned} $$

Multiply $ \dfrac{75x^2}{50} $ by $ x^2 $ to get $ \dfrac{ 75x^4 }{ 50 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{75x^2}{50} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{75x^2}{50} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 75x^2 \cdot x^2 }{ 50 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 75x^4 }{ 50 } \end{aligned} $$

Subtract $25x$ from $ \dfrac{75x^4}{50} $ to get $ \dfrac{ \color{purple}{ 75x^4-1250x } }{ 50 }$.

Step 1: Write $ 25x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{50}$.

$$ \begin{aligned} \frac{75x^4}{50} -25x & \xlongequal{\text{Step 1}} \frac{75x^4}{50} - \frac{25x}{\color{red}{1}} = \frac{ 75x^4 }{ 50 } - \frac{ 25x \cdot \color{blue}{ 50 }}{ 1 \cdot \color{blue}{ 50 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 75x^4 } }{ 50 } - \frac{ \color{purple}{ 1250x } }{ 50 }=\frac{ \color{purple}{ 75x^4-1250x } }{ 50 } \end{aligned} $$