Find $ \left(x+3\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}{ 3 }$.

$$ \begin{aligned}\left(x+3\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 3 + \color{red}{3^2} = x^2+6x+9\end{aligned} $$

Find $ \left(x+6\right)^3 $ using formula

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

where $ A = x $ and $ B = 6 $.

$$ \left(x+6\right)^3 = x^3+3 \cdot x^2 \cdot 6 + 3 \cdot x \cdot 6^2+6^3 = x^3+18x^2+108x+216 $$

Multiply each term of $ \left( \color{blue}{x^2+6x+9}\right) $ by each term in $ \left( x-5\right) $.

$$ \left( \color{blue}{x^2+6x+9}\right) \cdot \left( x-5\right) = x^3-5x^2+6x^2-30x+9x-45 $$

Combine like terms:

$$ x^3 \color{blue}{-5x^2} + \color{blue}{6x^2} \color{red}{-30x} + \color{red}{9x} -45 = x^3+ \color{blue}{x^2} \color{red}{-21x} -45 $$

Multiply each term of $ \left( \color{blue}{x^3+x^2-21x-45}\right) $ by each term in $ \left( x^3+18x^2+108x+216\right) $.

$$ \left( \color{blue}{x^3+x^2-21x-45}\right) \cdot \left( x^3+18x^2+108x+216\right) = \\ = x^6+18x^5+108x^4+216x^3+x^5+18x^4+108x^3+216x^2-21x^4-378x^3-2268x^2-4536x-45x^3-810x^2-4860x-9720 $$

Combine like terms:

$$ x^6+ \color{blue}{18x^5} + \color{red}{108x^4} + \color{green}{216x^3} + \color{blue}{x^5} + \color{orange}{18x^4} + \color{blue}{108x^3} + \color{red}{216x^2} \color{orange}{-21x^4} \color{green}{-378x^3} \color{orange}{-2268x^2} \color{blue}{-4536x} \color{green}{-45x^3} \color{orange}{-810x^2} \color{blue}{-4860x} -9720 = \\ = x^6+ \color{blue}{19x^5} + \color{orange}{105x^4} \color{green}{-99x^3} \color{orange}{-2862x^2} \color{blue}{-9396x} -9720 $$