Find $ \left(x-5\right)^2 $ using formula.

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

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 5 }$.

$$ \begin{aligned}\left(x-5\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 5 + \color{red}{5^2} = x^2-10x+25\end{aligned} $$

Find $ \left(3x-2\right)^3 $ using formula

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

where $ A = 3x $ and $ B = 2 $.

$$ \left(3x-2\right)^3 = \left( 3x \right)^3-3 \cdot \left( 3x \right)^2 \cdot 2 + 3 \cdot 3x \cdot 2^2-2^3 = 27x^3-54x^2+36x-8 $$

Multiply $ \color{blue}{3} $ by $ \left( x+6\right) $ $$ \color{blue}{3} \cdot \left( x+6\right) = 3x+18 $$

Multiply each term of $ \left( \color{blue}{3x+18}\right) $ by each term in $ \left( x^2-10x+25\right) $.

$$ \left( \color{blue}{3x+18}\right) \cdot \left( x^2-10x+25\right) = 3x^3-30x^2+75x+18x^2-180x+450 $$

Combine like terms:

$$ 3x^3 \color{blue}{-30x^2} + \color{red}{75x} + \color{blue}{18x^2} \color{red}{-180x} +450 = 3x^3 \color{blue}{-12x^2} \color{red}{-105x} +450 $$

Multiply each term of $ \left( \color{blue}{3x^3-12x^2-105x+450}\right) $ by each term in $ \left( 27x^3-54x^2+36x-8\right) $.

$$ \left( \color{blue}{3x^3-12x^2-105x+450}\right) \cdot \left( 27x^3-54x^2+36x-8\right) = \\ = 81x^6-162x^5+108x^4-24x^3-324x^5+648x^4-432x^3+96x^2-2835x^4+5670x^3-3780x^2+840x+12150x^3-24300x^2+16200x-3600 $$

Combine like terms:

$$ 81x^6 \color{blue}{-162x^5} + \color{red}{108x^4} \color{green}{-24x^3} \color{blue}{-324x^5} + \color{orange}{648x^4} \color{blue}{-432x^3} + \color{red}{96x^2} \color{orange}{-2835x^4} + \color{green}{5670x^3} \color{orange}{-3780x^2} + \color{blue}{840x} + \color{green}{12150x^3} \color{orange}{-24300x^2} + \color{blue}{16200x} -3600 = \\ = 81x^6 \color{blue}{-486x^5} \color{orange}{-2079x^4} + \color{green}{17364x^3} \color{orange}{-27984x^2} + \color{blue}{17040x} -3600 $$