Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x-1}\right) \cdot \left( x-4\right) = x^2-4x-x+4 $$

Combine like terms:

$$ x^2 \color{blue}{-4x} \color{blue}{-x} +4 = x^2 \color{blue}{-5x} +4 $$

Multiply each term of $ \left( \color{blue}{x^2-5x+4}\right) $ by each term in $ \left( x+2\right) $.

$$ \left( \color{blue}{x^2-5x+4}\right) \cdot \left( x+2\right) = x^3+2x^2-5x^2-10x+4x+8 $$

Combine like terms:

$$ x^3+ \color{blue}{2x^2} \color{blue}{-5x^2} \color{red}{-10x} + \color{red}{4x} +8 = x^3 \color{blue}{-3x^2} \color{red}{-6x} +8 $$

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

$$ \left( \color{blue}{x^3-3x^2-6x+8}\right) \cdot \left( x+3\right) = \\ = x^4+ \cancel{3x^3} -\cancel{3x^3}-9x^2-6x^2-18x+8x+24 $$

Combine like terms:

$$ x^4+ \, \color{blue}{ \cancel{3x^3}} \, \, \color{blue}{ -\cancel{3x^3}} \, \color{green}{-9x^2} \color{green}{-6x^2} \color{orange}{-18x} + \color{orange}{8x} +24 = x^4 \color{green}{-15x^2} \color{orange}{-10x} +24 $$