Find $ \left(x-1\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}{ 1 }$.

$$ \begin{aligned}\left(x-1\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 1 + \color{red}{1^2} = x^2-2x+1\end{aligned} $$

Find $ \left(x-2\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}{ 2 }$.

$$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$

Multiply $ \color{blue}{x} $ by $ \left( x^2-2x+1\right) $ $$ \color{blue}{x} \cdot \left( x^2-2x+1\right) = x^3-2x^2+x $$

Multiply each term of $ \left( \color{blue}{x^3-2x^2+x}\right) $ by each term in $ \left( x^2-4x+4\right) $.

$$ \left( \color{blue}{x^3-2x^2+x}\right) \cdot \left( x^2-4x+4\right) = x^5-4x^4+4x^3-2x^4+8x^3-8x^2+x^3-4x^2+4x $$

Combine like terms:

$$ x^5 \color{blue}{-4x^4} + \color{red}{4x^3} \color{blue}{-2x^4} + \color{green}{8x^3} \color{orange}{-8x^2} + \color{green}{x^3} \color{orange}{-4x^2} +4x = \\ = x^5 \color{blue}{-6x^4} + \color{green}{13x^3} \color{orange}{-12x^2} +4x $$

Multiply each term of $ \left( \color{blue}{x^5-6x^4+13x^3-12x^2+4x}\right) $ by each term in $ \left( x-3\right) $.

$$ \left( \color{blue}{x^5-6x^4+13x^3-12x^2+4x}\right) \cdot \left( x-3\right) = \\ = x^6-3x^5-6x^5+18x^4+13x^4-39x^3-12x^3+36x^2+4x^2-12x $$

Combine like terms:

$$ x^6 \color{blue}{-3x^5} \color{blue}{-6x^5} + \color{red}{18x^4} + \color{red}{13x^4} \color{green}{-39x^3} \color{green}{-12x^3} + \color{orange}{36x^2} + \color{orange}{4x^2} -12x = \\ = x^6 \color{blue}{-9x^5} + \color{red}{31x^4} \color{green}{-51x^3} + \color{orange}{40x^2} -12x $$