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-5\right)^3 $ using formula

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

where $ A = x $ and $ B = 5 $.

$$ \left(x-5\right)^3 = x^3-3 \cdot x^2 \cdot 5 + 3 \cdot x \cdot 5^2-5^3 = x^3-15x^2+75x-125 $$

Multiply each term of $ \left( \color{blue}{x^2+2x+1}\right) $ by each term in $ \left( x^3-15x^2+75x-125\right) $.

$$ \left( \color{blue}{x^2+2x+1}\right) \cdot \left( x^3-15x^2+75x-125\right) = \\ = x^5-15x^4+75x^3-125x^2+2x^4-30x^3+150x^2-250x+x^3-15x^2+75x-125 $$

Combine like terms:

$$ x^5 \color{blue}{-15x^4} + \color{red}{75x^3} \color{green}{-125x^2} + \color{blue}{2x^4} \color{orange}{-30x^3} + \color{blue}{150x^2} \color{red}{-250x} + \color{orange}{x^3} \color{blue}{-15x^2} + \color{red}{75x} -125 = \\ = x^5 \color{blue}{-13x^4} + \color{orange}{46x^3} + \color{blue}{10x^2} \color{red}{-175x} -125 $$

Multiply each term of $ \left( \color{blue}{x^5-13x^4+46x^3+10x^2-175x-125}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x^5-13x^4+46x^3+10x^2-175x-125}\right) \cdot \left( x-4\right) = \\ = x^6-4x^5-13x^5+52x^4+46x^4-184x^3+10x^3-40x^2-175x^2+700x-125x+500 $$

Combine like terms:

$$ x^6 \color{blue}{-4x^5} \color{blue}{-13x^5} + \color{red}{52x^4} + \color{red}{46x^4} \color{green}{-184x^3} + \color{green}{10x^3} \color{orange}{-40x^2} \color{orange}{-175x^2} + \color{blue}{700x} \color{blue}{-125x} +500 = \\ = x^6 \color{blue}{-17x^5} + \color{red}{98x^4} \color{green}{-174x^3} \color{orange}{-215x^2} + \color{blue}{575x} +500 $$