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-3\right)^3 $ using formula

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

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

$$ \left(x-3\right)^3 = x^3-3 \cdot x^2 \cdot 3 + 3 \cdot x \cdot 3^2-3^3 = x^3-9x^2+27x-27 $$

Multiply each term of $ \left( \color{blue}{x^2+2x+1}\right) $ by each term in $ \left( x^3-9x^2+27x-27\right) $.

$$ \left( \color{blue}{x^2+2x+1}\right) \cdot \left( x^3-9x^2+27x-27\right) = \\ = x^5-9x^4+27x^3-27x^2+2x^4-18x^3+54x^2-54x+x^3-9x^2+27x-27 $$

Combine like terms:

$$ x^5 \color{blue}{-9x^4} + \color{red}{27x^3} \color{green}{-27x^2} + \color{blue}{2x^4} \color{orange}{-18x^3} + \color{blue}{54x^2} \color{red}{-54x} + \color{orange}{x^3} \color{blue}{-9x^2} + \color{red}{27x} -27 = \\ = x^5 \color{blue}{-7x^4} + \color{orange}{10x^3} + \color{blue}{18x^2} \color{red}{-27x} -27 $$

Multiply each term of $ \left( \color{blue}{x^5-7x^4+10x^3+18x^2-27x-27}\right) $ by each term in $ \left( x-2\right) $.

$$ \left( \color{blue}{x^5-7x^4+10x^3+18x^2-27x-27}\right) \cdot \left( x-2\right) = \\ = x^6-2x^5-7x^5+14x^4+10x^4-20x^3+18x^3-36x^2-27x^2+54x-27x+54 $$

Combine like terms:

$$ x^6 \color{blue}{-2x^5} \color{blue}{-7x^5} + \color{red}{14x^4} + \color{red}{10x^4} \color{green}{-20x^3} + \color{green}{18x^3} \color{orange}{-36x^2} \color{orange}{-27x^2} + \color{blue}{54x} \color{blue}{-27x} +54 = \\ = x^6 \color{blue}{-9x^5} + \color{red}{24x^4} \color{green}{-2x^3} \color{orange}{-63x^2} + \color{blue}{27x} +54 $$