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

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

Combine like terms:

$$ x^2+ \color{blue}{2x} + \color{blue}{4x} +8 = x^2+ \color{blue}{6x} +8 $$

Multiply each term of $ \left( \color{blue}{x^2+6x+8}\right) $ by each term in $ \left( x+1\right) $.

$$ \left( \color{blue}{x^2+6x+8}\right) \cdot \left( x+1\right) = x^3+x^2+6x^2+6x+8x+8 $$

Combine like terms:

$$ x^3+ \color{blue}{x^2} + \color{blue}{6x^2} + \color{red}{6x} + \color{red}{8x} +8 = x^3+ \color{blue}{7x^2} + \color{red}{14x} +8 $$

Multiply each term of $ \left( \color{blue}{x^3+7x^2+14x+8}\right) $ by each term in $ \left( x-1\right) $.

$$ \left( \color{blue}{x^3+7x^2+14x+8}\right) \cdot \left( x-1\right) = x^4-x^3+7x^3-7x^2+14x^2-14x+8x-8 $$

Combine like terms:

$$ x^4 \color{blue}{-x^3} + \color{blue}{7x^3} \color{red}{-7x^2} + \color{red}{14x^2} \color{green}{-14x} + \color{green}{8x} -8 = x^4+ \color{blue}{6x^3} + \color{red}{7x^2} \color{green}{-6x} -8 $$

Multiply each term of $ \left( \color{blue}{x^4+6x^3+7x^2-6x-8}\right) $ by each term in $ \left( x-4\right) $.

$$ \left( \color{blue}{x^4+6x^3+7x^2-6x-8}\right) \cdot \left( x-4\right) = x^5-4x^4+6x^4-24x^3+7x^3-28x^2-6x^2+24x-8x+32 $$

Combine like terms:

$$ x^5 \color{blue}{-4x^4} + \color{blue}{6x^4} \color{red}{-24x^3} + \color{red}{7x^3} \color{green}{-28x^2} \color{green}{-6x^2} + \color{orange}{24x} \color{orange}{-8x} +32 = \\ = x^5+ \color{blue}{2x^4} \color{red}{-17x^3} \color{green}{-34x^2} + \color{orange}{16x} +32 $$