Find $ \left(-3x+18\right)^2 $ in two steps.

S1: Change all signs inside bracket.

S2: Apply formula

$$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 18 }$.

$$ \begin{aligned}\left(-3x+18\right)^2& \xlongequal{ S1 } \left(3x-18\right)^2 \xlongequal{ S2 } \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 18 + \color{red}{18^2} = \\[1 em] & = 9x^2-108x+324\end{aligned} $$

Find $ \left(-3x+18\right)^2 $ in two steps.

S1: Change all signs inside bracket.

S2: Apply formula

$$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 18 }$.

$$ \begin{aligned}\left(-3x+18\right)^2& \xlongequal{ S1 } \left(3x-18\right)^2 \xlongequal{ S2 } \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 18 + \color{red}{18^2} = \\[1 em] & = 9x^2-108x+324\end{aligned} $$

Find $ \left(-3x+18\right)^3 $ in two steps.

S1: Swap two terms inside bracket

S2: apply formula

$$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$

where $ A = 18 $ and $ B = 3x $.

$$ \left(-3x+18\right)^3 \xlongequal{ S1 } \left(18-3x\right)^3 = 18^3-3 \cdot 18^2 \cdot 3x + 3 \cdot 18 \cdot \left( 3x \right)^2-\left( 3x \right)^3 = 5832-2916x+486x^2-27x^3 $$

Multiply $3$ by $ \dfrac{9x^2-108x+324}{2} $ to get $ \dfrac{ 27x^2-324x+972 }{ 2 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3 \cdot \frac{9x^2-108x+324}{2} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{9x^2-108x+324}{2} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( 9x^2-108x+324 \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 27x^2-324x+972 }{ 2 } \end{aligned} $$

Multiply $x$ by $ \dfrac{9x^2-108x+324}{4} $ to get $ \dfrac{ 9x^3-108x^2+324x }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} x \cdot \frac{9x^2-108x+324}{4} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} \cdot \frac{9x^2-108x+324}{4} \xlongequal{\text{Step 2}} \frac{ x \cdot \left( 9x^2-108x+324 \right) }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^3-108x^2+324x }{ 4 } \end{aligned} $$

Find $ \left(-3x+18\right)^3 $ in two steps.

S1: Swap two terms inside bracket

S2: apply formula

$$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$

where $ A = 18 $ and $ B = 3x $.

$$ \left(-3x+18\right)^3 \xlongequal{ S1 } \left(18-3x\right)^3 = 18^3-3 \cdot 18^2 \cdot 3x + 3 \cdot 18 \cdot \left( 3x \right)^2-\left( 3x \right)^3 = 5832-2916x+486x^2-27x^3 $$

Subtract $ \dfrac{9x^3-108x^2+324x}{4} $ from $ \dfrac{27x^2-324x+972}{2} $ to get $ \dfrac{ \color{purple}{ -9x^3+162x^2-972x+1944 } }{ 4 }$.

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

$$ \begin{aligned} \frac{27x^2-324x+972}{2} - \frac{9x^3-108x^2+324x}{4} & = \frac{ \left( 27x^2-324x+972 \right) \cdot \color{blue}{ 2 }}{ 2 \cdot \color{blue}{ 2 }} - \frac{ 9x^3-108x^2+324x }{ 4 } = \\[1ex] &=\frac{ \color{purple}{ 54x^2-648x+1944 } }{ 4 } - \frac{ \color{purple}{ 9x^3-108x^2+324x } }{ 4 }=\frac{ \color{purple}{ 54x^2-648x+1944 - \left( 9x^3-108x^2+324x \right) } }{ 4 } = \\[1ex] &=\frac{ \color{purple}{ -9x^3+162x^2-972x+1944 } }{ 4 } \end{aligned} $$

Find $ \left(-3x+18\right)^3 $ in two steps.

S1: Swap two terms inside bracket

S2: apply formula

$$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$

where $ A = 18 $ and $ B = 3x $.

$$ \left(-3x+18\right)^3 \xlongequal{ S1 } \left(18-3x\right)^3 = 18^3-3 \cdot 18^2 \cdot 3x + 3 \cdot 18 \cdot \left( 3x \right)^2-\left( 3x \right)^3 = 5832-2916x+486x^2-27x^3 $$

Subtract $ \dfrac{5832-2916x+486x^2-27x^3}{18} $ from $ \dfrac{-9x^3+162x^2-972x+1944}{4} $ to get $ \dfrac{ \color{purple}{ -27x^3+486x^2-2916x+5832 } }{ 36 }$.

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 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{-9x^3+162x^2-972x+1944}{4} - \frac{5832-2916x+486x^2-27x^3}{18} & = \frac{ \left( -9x^3+162x^2-972x+1944 \right) \cdot \color{blue}{ 9 }}{ 4 \cdot \color{blue}{ 9 }} - \frac{ \left( 5832-2916x+486x^2-27x^3 \right) \cdot \color{blue}{ 2 }}{ 18 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -81x^3+1458x^2-8748x+17496 } }{ 36 } - \frac{ \color{purple}{ 11664-5832x+972x^2-54x^3 } }{ 36 } = \\[1ex] &=\frac{ \color{purple}{ -81x^3+1458x^2-8748x+17496 - \left( 11664-5832x+972x^2-54x^3 \right) } }{ 36 } = \\[1ex] &=\frac{ \color{purple}{ -27x^3+486x^2-2916x+5832 } }{ 36 } \end{aligned} $$

Multiply $x$ by $ \dfrac{-27x^3+486x^2-2916x+5832}{36} $ to get $ \dfrac{ -27x^4+486x^3-2916x^2+5832x }{ 36 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} x \cdot \frac{-27x^3+486x^2-2916x+5832}{36} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} \cdot \frac{-27x^3+486x^2-2916x+5832}{36} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ x \cdot \left( -27x^3+486x^2-2916x+5832 \right) }{ 1 \cdot 36 } \xlongequal{\text{Step 3}} \frac{ -27x^4+486x^3-2916x^2+5832x }{ 36 } \end{aligned} $$