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

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

Combine like terms:

$$ x^2 \color{blue}{-4x} \color{blue}{-3x} +12 = x^2 \color{blue}{-7x} +12 $$

Multiply each term of $ \left( \color{blue}{x^2-7x+12}\right) $ by each term in $ \left( x-6\right) $.

$$ \left( \color{blue}{x^2-7x+12}\right) \cdot \left( x-6\right) = x^3-6x^2-7x^2+42x+12x-72 $$

Combine like terms:

$$ x^3 \color{blue}{-6x^2} \color{blue}{-7x^2} + \color{red}{42x} + \color{red}{12x} -72 = x^3 \color{blue}{-13x^2} + \color{red}{54x} -72 $$

Multiply each term of $ \left( \color{blue}{x^3-13x^2+54x-72}\right) $ by each term in $ \left( x-8\right) $.

$$ \left( \color{blue}{x^3-13x^2+54x-72}\right) \cdot \left( x-8\right) = x^4-8x^3-13x^3+104x^2+54x^2-432x-72x+576 $$

Combine like terms:

$$ x^4 \color{blue}{-8x^3} \color{blue}{-13x^3} + \color{red}{104x^2} + \color{red}{54x^2} \color{green}{-432x} \color{green}{-72x} +576 = \\ = x^4 \color{blue}{-21x^3} + \color{red}{158x^2} \color{green}{-504x} +576 $$

Multiply each term of $ \left( \color{blue}{x^4-21x^3+158x^2-504x+576}\right) $ by each term in $ \left( x-10\right) $.

$$ \left( \color{blue}{x^4-21x^3+158x^2-504x+576}\right) \cdot \left( x-10\right) = \\ = x^5-10x^4-21x^4+210x^3+158x^3-1580x^2-504x^2+5040x+576x-5760 $$

Combine like terms:

$$ x^5 \color{blue}{-10x^4} \color{blue}{-21x^4} + \color{red}{210x^3} + \color{red}{158x^3} \color{green}{-1580x^2} \color{green}{-504x^2} + \color{orange}{5040x} + \color{orange}{576x} -5760 = \\ = x^5 \color{blue}{-31x^4} + \color{red}{368x^3} \color{green}{-2084x^2} + \color{orange}{5616x} -5760 $$