Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x-1}\right) \cdot \left( x-4\right) = x^2-4x-x+4 $$

Combine like terms:

$$ x^2 \color{blue}{-4x} \color{blue}{-x} +4 = x^2 \color{blue}{-5x} +4 $$

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

$$ \left( \color{blue}{x^2-5x+4}\right) \cdot \left( x-6\right) = x^3-6x^2-5x^2+30x+4x-24 $$

Combine like terms:

$$ x^3 \color{blue}{-6x^2} \color{blue}{-5x^2} + \color{red}{30x} + \color{red}{4x} -24 = x^3 \color{blue}{-11x^2} + \color{red}{34x} -24 $$

Multiply each term of $ \left( \color{blue}{x^3-11x^2+34x-24}\right) $ by each term in $ \left( x-8\right) $.

$$ \left( \color{blue}{x^3-11x^2+34x-24}\right) \cdot \left( x-8\right) = x^4-8x^3-11x^3+88x^2+34x^2-272x-24x+192 $$

Combine like terms:

$$ x^4 \color{blue}{-8x^3} \color{blue}{-11x^3} + \color{red}{88x^2} + \color{red}{34x^2} \color{green}{-272x} \color{green}{-24x} +192 = \\ = x^4 \color{blue}{-19x^3} + \color{red}{122x^2} \color{green}{-296x} +192 $$

Multiply each term of $ \left( \color{blue}{x^4-19x^3+122x^2-296x+192}\right) $ by each term in $ \left( x-10\right) $.

$$ \left( \color{blue}{x^4-19x^3+122x^2-296x+192}\right) \cdot \left( x-10\right) = \\ = x^5-10x^4-19x^4+190x^3+122x^3-1220x^2-296x^2+2960x+192x-1920 $$

Combine like terms:

$$ x^5 \color{blue}{-10x^4} \color{blue}{-19x^4} + \color{red}{190x^3} + \color{red}{122x^3} \color{green}{-1220x^2} \color{green}{-296x^2} + \color{orange}{2960x} + \color{orange}{192x} -1920 = \\ = x^5 \color{blue}{-29x^4} + \color{red}{312x^3} \color{green}{-1516x^2} + \color{orange}{3152x} -1920 $$