Find $ \left(x+4\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}{ 4 }$.

$$ \begin{aligned}\left(x+4\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 4 + \color{red}{4^2} = x^2+8x+16\end{aligned} $$

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+8x+16}\right) $ by each term in $ \left( x^3-9x^2+27x-27\right) $.

$$ \left( \color{blue}{x^2+8x+16}\right) \cdot \left( x^3-9x^2+27x-27\right) = \\ = x^5-9x^4+27x^3-27x^2+8x^4-72x^3+216x^2-216x+16x^3-144x^2+432x-432 $$

Combine like terms:

$$ x^5 \color{blue}{-9x^4} + \color{red}{27x^3} \color{green}{-27x^2} + \color{blue}{8x^4} \color{orange}{-72x^3} + \color{blue}{216x^2} \color{red}{-216x} + \color{orange}{16x^3} \color{blue}{-144x^2} + \color{red}{432x} -432 = \\ = x^5 \color{blue}{-x^4} \color{orange}{-29x^3} + \color{blue}{45x^2} + \color{red}{216x} -432 $$

Multiply each term of $ \left( \color{blue}{x^5-x^4-29x^3+45x^2+216x-432}\right) $ by each term in $ \left( x-2\right) $.

$$ \left( \color{blue}{x^5-x^4-29x^3+45x^2+216x-432}\right) \cdot \left( x-2\right) = \\ = x^6-2x^5-x^5+2x^4-29x^4+58x^3+45x^3-90x^2+216x^2-432x-432x+864 $$

Combine like terms:

$$ x^6 \color{blue}{-2x^5} \color{blue}{-x^5} + \color{red}{2x^4} \color{red}{-29x^4} + \color{green}{58x^3} + \color{green}{45x^3} \color{orange}{-90x^2} + \color{orange}{216x^2} \color{blue}{-432x} \color{blue}{-432x} +864 = \\ = x^6 \color{blue}{-3x^5} \color{red}{-27x^4} + \color{green}{103x^3} + \color{orange}{126x^2} \color{blue}{-864x} +864 $$