Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x-1\right) $.

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

Combine like terms:

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

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

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

Combine like terms:

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

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

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

Combine like terms:

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

Multiply each term of $ \left( \color{blue}{x^4-4x^3-x^2+16x-12}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x^4-4x^3-x^2+16x-12}\right) \cdot \left( x-4\right) = x^5-4x^4-4x^4+16x^3-x^3+4x^2+16x^2-64x-12x+48 $$

Combine like terms:

$$ x^5 \color{blue}{-4x^4} \color{blue}{-4x^4} + \color{red}{16x^3} \color{red}{-x^3} + \color{green}{4x^2} + \color{green}{16x^2} \color{orange}{-64x} \color{orange}{-12x} +48 = \\ = x^5 \color{blue}{-8x^4} + \color{red}{15x^3} + \color{green}{20x^2} \color{orange}{-76x} +48 $$