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-8\right) $.

$$ \left( \color{blue}{x^3-8x^2+19x-12}\right) \cdot \left( x-8\right) = x^4-8x^3-8x^3+64x^2+19x^2-152x-12x+96 $$

Combine like terms:

$$ x^4 \color{blue}{-8x^3} \color{blue}{-8x^3} + \color{red}{64x^2} + \color{red}{19x^2} \color{green}{-152x} \color{green}{-12x} +96 = \\ = x^4 \color{blue}{-16x^3} + \color{red}{83x^2} \color{green}{-164x} +96 $$

Multiply each term of $ \left( \color{blue}{x^4-16x^3+83x^2-164x+96}\right) $ by each term in $ \left( x-10\right) $.

$$ \left( \color{blue}{x^4-16x^3+83x^2-164x+96}\right) \cdot \left( x-10\right) = \\ = x^5-10x^4-16x^4+160x^3+83x^3-830x^2-164x^2+1640x+96x-960 $$

Combine like terms:

$$ x^5 \color{blue}{-10x^4} \color{blue}{-16x^4} + \color{red}{160x^3} + \color{red}{83x^3} \color{green}{-830x^2} \color{green}{-164x^2} + \color{orange}{1640x} + \color{orange}{96x} -960 = \\ = x^5 \color{blue}{-26x^4} + \color{red}{243x^3} \color{green}{-994x^2} + \color{orange}{1736x} -960 $$