Multiply $ \dfrac{9a^2-36a+25}{9} $ by $ a^2 $ to get $ \dfrac{ 9a^4-36a^3+25a^2 }{ 9 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{9a^2-36a+25}{9} \cdot a^2 & \xlongequal{\text{Step 1}} \frac{9a^2-36a+25}{9} \cdot \frac{a^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 9a^2-36a+25 \right) \cdot a^2 }{ 9 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9a^4-36a^3+25a^2 }{ 9 } \end{aligned} $$

Subtract $25$ from $ \dfrac{9a^4-36a^3+25a^2}{9} $ to get $ \dfrac{ \color{purple}{ 9a^4-36a^3+25a^2-225 } }{ 9 }$.

Step 1: Write $ 25 $ 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 $\color{blue}{9}$.

$$ \begin{aligned} \frac{9a^4-36a^3+25a^2}{9} -25 & \xlongequal{\text{Step 1}} \frac{9a^4-36a^3+25a^2}{9} - \frac{25}{\color{red}{1}} = \frac{ 9a^4-36a^3+25a^2 }{ 9 } - \frac{ 25 \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9a^4-36a^3+25a^2 } }{ 9 } - \frac{ \color{purple}{ 225 } }{ 9 }=\frac{ \color{purple}{ 9a^4-36a^3+25a^2-225 } }{ 9 } \end{aligned} $$