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

$$ \left( \color{blue}{x-1}\right) \cdot \left( x-3\right) = x^2-3x-x+3 $$

Combine like terms:

$$ x^2 \color{blue}{-3x} \color{blue}{-x} +3 = x^2 \color{blue}{-4x} +3 $$

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

$$ \left( \color{blue}{x^2-4x+3}\right) \cdot \left( x-4\right) = x^3-4x^2-4x^2+16x+3x-12 $$

Combine like terms:

$$ x^3 \color{blue}{-4x^2} \color{blue}{-4x^2} + \color{red}{16x} + \color{red}{3x} -12 = x^3 \color{blue}{-8x^2} + \color{red}{19x} -12 $$

Multiply each term of $ \left( \color{blue}{x^3-8x^2+19x-12}\right) $ by each term in $ \left( x-6\right) $.

$$ \left( \color{blue}{x^3-8x^2+19x-12}\right) \cdot \left( x-6\right) = x^4-6x^3-8x^3+48x^2+19x^2-114x-12x+72 $$

Combine like terms:

$$ x^4 \color{blue}{-6x^3} \color{blue}{-8x^3} + \color{red}{48x^2} + \color{red}{19x^2} \color{green}{-114x} \color{green}{-12x} +72 = \\ = x^4 \color{blue}{-14x^3} + \color{red}{67x^2} \color{green}{-126x} +72 $$

Multiply each term of $ \left( \color{blue}{x^4-14x^3+67x^2-126x+72}\right) $ by each term in $ \left( x-8\right) $.

$$ \left( \color{blue}{x^4-14x^3+67x^2-126x+72}\right) \cdot \left( x-8\right) = \\ = x^5-8x^4-14x^4+112x^3+67x^3-536x^2-126x^2+1008x+72x-576 $$

Combine like terms:

$$ x^5 \color{blue}{-8x^4} \color{blue}{-14x^4} + \color{red}{112x^3} + \color{red}{67x^3} \color{green}{-536x^2} \color{green}{-126x^2} + \color{orange}{1008x} + \color{orange}{72x} -576 = \\ = x^5 \color{blue}{-22x^4} + \color{red}{179x^3} \color{green}{-662x^2} + \color{orange}{1080x} -576 $$