Multiply each term of $ \left( \color{blue}{x-3}\right) $ by each term in $ \left( 7x^7+6x^6+5x^5+4x^4+3x^3+2x^2+x+1\right) $.

$$ \left( \color{blue}{x-3}\right) \cdot \left( 7x^7+6x^6+5x^5+4x^4+3x^3+2x^2+x+1\right) = \\ = 7x^8+6x^7+5x^6+4x^5+3x^4+2x^3+x^2+x-21x^7-18x^6-15x^5-12x^4-9x^3-6x^2-3x-3 $$

Combine like terms:

$$ 7x^8+ \color{blue}{6x^7} + \color{red}{5x^6} + \color{green}{4x^5} + \color{orange}{3x^4} + \color{blue}{2x^3} + \color{red}{x^2} + \color{green}{x} \color{blue}{-21x^7} \color{red}{-18x^6} \color{green}{-15x^5} \color{orange}{-12x^4} \color{blue}{-9x^3} \color{red}{-6x^2} \color{green}{-3x} -3 = \\ = 7x^8 \color{blue}{-15x^7} \color{red}{-13x^6} \color{green}{-11x^5} \color{orange}{-9x^4} \color{blue}{-7x^3} \color{red}{-5x^2} \color{green}{-2x} -3 $$