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-6\right) $.

$$ \left( \color{blue}{x^2-4x+3}\right) \cdot \left( x-6\right) = x^3-6x^2-4x^2+24x+3x-18 $$

Combine like terms:

$$ x^3 \color{blue}{-6x^2} \color{blue}{-4x^2} + \color{red}{24x} + \color{red}{3x} -18 = x^3 \color{blue}{-10x^2} + \color{red}{27x} -18 $$

Multiply each term of $ \left( \color{blue}{x^3-10x^2+27x-18}\right) $ by each term in $ \left( x-8\right) $.

$$ \left( \color{blue}{x^3-10x^2+27x-18}\right) \cdot \left( x-8\right) = x^4-8x^3-10x^3+80x^2+27x^2-216x-18x+144 $$

Combine like terms:

$$ x^4 \color{blue}{-8x^3} \color{blue}{-10x^3} + \color{red}{80x^2} + \color{red}{27x^2} \color{green}{-216x} \color{green}{-18x} +144 = \\ = x^4 \color{blue}{-18x^3} + \color{red}{107x^2} \color{green}{-234x} +144 $$

Multiply each term of $ \left( \color{blue}{x^4-18x^3+107x^2-234x+144}\right) $ by each term in $ \left( x-10\right) $.

$$ \left( \color{blue}{x^4-18x^3+107x^2-234x+144}\right) \cdot \left( x-10\right) = \\ = x^5-10x^4-18x^4+180x^3+107x^3-1070x^2-234x^2+2340x+144x-1440 $$

Combine like terms:

$$ x^5 \color{blue}{-10x^4} \color{blue}{-18x^4} + \color{red}{180x^3} + \color{red}{107x^3} \color{green}{-1070x^2} \color{green}{-234x^2} + \color{orange}{2340x} + \color{orange}{144x} -1440 = \\ = x^5 \color{blue}{-28x^4} + \color{red}{287x^3} \color{green}{-1304x^2} + \color{orange}{2484x} -1440 $$