Multiply $ \color{blue}{x} $ by $ \left( x+10\right) $ $$ \color{blue}{x} \cdot \left( x+10\right) = x^2+10x $$

Multiply each term of $ \left( \color{blue}{x^2+10x}\right) $ by each term in $ \left( x+15\right) $.

$$ \left( \color{blue}{x^2+10x}\right) \cdot \left( x+15\right) = x^3+15x^2+10x^2+150x $$

Combine like terms:

$$ x^3+ \color{blue}{15x^2} + \color{blue}{10x^2} +150x = x^3+ \color{blue}{25x^2} +150x $$

Multiply each term of $ \left( \color{blue}{x^3+25x^2+150x}\right) $ by each term in $ \left( x+20\right) $.

$$ \left( \color{blue}{x^3+25x^2+150x}\right) \cdot \left( x+20\right) = x^4+20x^3+25x^3+500x^2+150x^2+3000x $$

Combine like terms:

$$ x^4+ \color{blue}{20x^3} + \color{blue}{25x^3} + \color{red}{500x^2} + \color{red}{150x^2} +3000x = x^4+ \color{blue}{45x^3} + \color{red}{650x^2} +3000x $$

Multiply each term of $ \left( \color{blue}{x^4+45x^3+650x^2+3000x}\right) $ by each term in $ \left( x^2+35x+500\right) $.

$$ \left( \color{blue}{x^4+45x^3+650x^2+3000x}\right) \cdot \left( x^2+35x+500\right) = \\ = x^6+35x^5+500x^4+45x^5+1575x^4+22500x^3+650x^4+22750x^3+325000x^2+3000x^3+105000x^2+1500000x $$

Combine like terms:

$$ x^6+ \color{blue}{35x^5} + \color{red}{500x^4} + \color{blue}{45x^5} + \color{green}{1575x^4} + \color{orange}{22500x^3} + \color{green}{650x^4} + \color{blue}{22750x^3} + \color{red}{325000x^2} + \color{blue}{3000x^3} + \color{red}{105000x^2} +1500000x = \\ = x^6+ \color{blue}{80x^5} + \color{green}{2725x^4} + \color{blue}{48250x^3} + \color{red}{430000x^2} +1500000x $$