Multiply $ \dfrac{4x^2+9x+2}{16} $ by $ x^2 $ to get $ \dfrac{ 4x^4+9x^3+2x^2 }{ 16 } $.

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.

$$ \begin{aligned} \frac{4x^2+9x+2}{16} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{4x^2+9x+2}{16} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 4x^2+9x+2 \right) \cdot x^2 }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4x^4+9x^3+2x^2 }{ 16 } \end{aligned} $$

Subtract $1$ from $ \dfrac{4x^4+9x^3+2x^2}{16} $ to get $ \dfrac{ \color{purple}{ 4x^4+9x^3+2x^2-16 } }{ 16 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{16}$.

$$ \begin{aligned} \frac{4x^4+9x^3+2x^2}{16} -1 & \xlongequal{\text{Step 1}} \frac{4x^4+9x^3+2x^2}{16} - \frac{1}{\color{red}{1}} = \frac{ 4x^4+9x^3+2x^2 }{ 16 } - \frac{ 1 \cdot \color{blue}{ 16 }}{ 1 \cdot \color{blue}{ 16 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^4+9x^3+2x^2 } }{ 16 } - \frac{ \color{purple}{ 16 } }{ 16 }=\frac{ \color{purple}{ 4x^4+9x^3+2x^2-16 } }{ 16 } \end{aligned} $$