Multiply $ \dfrac{4}{3} $ by $ x^2 $ to get $ \dfrac{ 4x^2 }{ 3 } $.

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.

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

Subtract $ \dfrac{4x^2}{3} $ from $ x $ to get $ \dfrac{ \color{purple}{ -4x^2+3x } }{ 3 }$.

Step 1: Write $ x $ 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 first fraction by $\color{blue}{ 3 }$.

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

Subtract $75$ from $ \dfrac{-4x^2+3x}{3} $ to get $ \dfrac{ \color{purple}{ -4x^2+3x-225 } }{ 3 }$.

Step 1: Write $ 75 $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{-4x^2+3x}{3} -75 & \xlongequal{\text{Step 1}} \frac{-4x^2+3x}{3} - \frac{75}{\color{red}{1}} = \frac{ -4x^2+3x }{ 3 } - \frac{ 75 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -4x^2+3x } }{ 3 } - \frac{ \color{purple}{ 225 } }{ 3 }=\frac{ \color{purple}{ -4x^2+3x-225 } }{ 3 } \end{aligned} $$