Multiply each term of $ \left( \color{blue}{x+12}\right) $ by each term in $ \left( x+5\right) $.

$$ \left( \color{blue}{x+12}\right) \cdot \left( x+5\right) = x^2+5x+12x+60 $$

Combine like terms:

$$ x^2+ \color{blue}{5x} + \color{blue}{12x} +60 = x^2+ \color{blue}{17x} +60 $$

Multiply each term of $ \left( \color{blue}{x^2+17x+60}\right) $ by each term in $ \left( x+5\right) $.

$$ \left( \color{blue}{x^2+17x+60}\right) \cdot \left( x+5\right) = x^3+5x^2+17x^2+85x+60x+300 $$

Combine like terms:

$$ x^3+ \color{blue}{5x^2} + \color{blue}{17x^2} + \color{red}{85x} + \color{red}{60x} +300 = x^3+ \color{blue}{22x^2} + \color{red}{145x} +300 $$

Multiply each term of $ \left( \color{blue}{x^3+22x^2+145x+300}\right) $ by each term in $ \left( x-1\right) $.

$$ \left( \color{blue}{x^3+22x^2+145x+300}\right) \cdot \left( x-1\right) = x^4-x^3+22x^3-22x^2+145x^2-145x+300x-300 $$

Combine like terms:

$$ x^4 \color{blue}{-x^3} + \color{blue}{22x^3} \color{red}{-22x^2} + \color{red}{145x^2} \color{green}{-145x} + \color{green}{300x} -300 = \\ = x^4+ \color{blue}{21x^3} + \color{red}{123x^2} + \color{green}{155x} -300 $$

Multiply each term of $ \left( \color{blue}{x^4+21x^3+123x^2+155x-300}\right) $ by each term in $ \left( x-7\right) $.

$$ \left( \color{blue}{x^4+21x^3+123x^2+155x-300}\right) \cdot \left( x-7\right) = \\ = x^5-7x^4+21x^4-147x^3+123x^3-861x^2+155x^2-1085x-300x+2100 $$

Combine like terms:

$$ x^5 \color{blue}{-7x^4} + \color{blue}{21x^4} \color{red}{-147x^3} + \color{red}{123x^3} \color{green}{-861x^2} + \color{green}{155x^2} \color{orange}{-1085x} \color{orange}{-300x} +2100 = \\ = x^5+ \color{blue}{14x^4} \color{red}{-24x^3} \color{green}{-706x^2} \color{orange}{-1385x} +2100 $$