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

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

$$ \left( \color{blue}{x^4-3x^3}\right) \cdot \left( x^2+4\right) = x^6+4x^4-3x^5-12x^3 $$

Multiply each term of $ \left( \color{blue}{x^6+4x^4-3x^5-12x^3}\right) $ by each term in $ \left( x^2-x-6\right) $.

$$ \left( \color{blue}{x^6+4x^4-3x^5-12x^3}\right) \cdot \left( x^2-x-6\right) = \\ = x^8-x^7-6x^6+4x^6-4x^5-24x^4-3x^7+3x^6+18x^5-12x^5+12x^4+72x^3 $$

Combine like terms:

$$ x^8 \color{blue}{-x^7} \color{red}{-6x^6} + \color{green}{4x^6} \color{orange}{-4x^5} \color{blue}{-24x^4} \color{blue}{-3x^7} + \color{green}{3x^6} + \color{red}{18x^5} \color{red}{-12x^5} + \color{blue}{12x^4} +72x^3 = \\ = x^8 \color{blue}{-4x^7} + \color{green}{x^6} + \color{red}{2x^5} \color{blue}{-12x^4} +72x^3 $$

Multiply each term of $ \left( \color{blue}{x^8-4x^7+x^6+2x^5-12x^4+72x^3}\right) $ by each term in $ \left( x^2-7\right) $.

$$ \left( \color{blue}{x^8-4x^7+x^6+2x^5-12x^4+72x^3}\right) \cdot \left( x^2-7\right) = \\ = x^{10}-7x^8-4x^9+28x^7+x^8-7x^6+2x^7-14x^5-12x^6+84x^4+72x^5-504x^3 $$

Combine like terms:

$$ x^{10} \color{blue}{-7x^8} -4x^9+ \color{red}{28x^7} + \color{blue}{x^8} \color{green}{-7x^6} + \color{red}{2x^7} \color{orange}{-14x^5} \color{green}{-12x^6} +84x^4+ \color{orange}{72x^5} -504x^3 = \\ = x^{10}-4x^9 \color{blue}{-6x^8} + \color{red}{30x^7} \color{green}{-19x^6} + \color{orange}{58x^5} +84x^4-504x^3 $$