Subtract $ \dfrac{44}{9} $ from $ t $ to get $ \dfrac{ \color{purple}{ 9t-44 } }{ 9 }$.

Step 1: Write $ t $ 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 $\color{blue}{ 9 }$.

$$ \begin{aligned} t- \frac{44}{9} & \xlongequal{\text{Step 1}} \frac{t}{\color{red}{1}} - \frac{44}{9} = \frac{ t \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} - \frac{ 44 }{ 9 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9t } }{ 9 } - \frac{ \color{purple}{ 44 } }{ 9 }=\frac{ \color{purple}{ 9t-44 } }{ 9 } \end{aligned} $$

Subtract $ \dfrac{22}{3} $ from $ t $ to get $ \dfrac{ \color{purple}{ 3t-22 } }{ 3 }$.

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

$$ \begin{aligned} t- \frac{22}{3} & \xlongequal{\text{Step 1}} \frac{t}{\color{red}{1}} - \frac{22}{3} = \frac{ t \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ 22 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3t } }{ 3 } - \frac{ \color{purple}{ 22 } }{ 3 }=\frac{ \color{purple}{ 3t-22 } }{ 3 } \end{aligned} $$

Multiply $ \dfrac{9t-44}{9} $ by $ \dfrac{3t-22}{3} $ to get $ \dfrac{27t^2-330t+968}{27} $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{9t-44}{9} \cdot \frac{3t-22}{3} & \xlongequal{\text{Step 1}} \frac{ \left( 9t-44 \right) \cdot \left( 3t-22 \right) }{ 9 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 27t^2-198t-132t+968 }{ 27 } = \frac{27t^2-330t+968}{27} \end{aligned} $$