Multiply each term of $ \left( \color{blue}{3x+1}\right) $ by each term in $ \left( x+1\right) $.

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

Combine like terms:

$$ 3x^2+ \color{blue}{3x} + \color{blue}{x} +1 = 3x^2+ \color{blue}{4x} +1 $$

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

$$ \left( \color{blue}{3x^2+4x+1}\right) \cdot \left( x-2\right) = 3x^3-6x^2+4x^2-8x+x-2 $$

Combine like terms:

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

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

$$ \left( \color{blue}{3x^3-2x^2-7x-2}\right) \cdot \left( 3x-2\right) = 9x^4-6x^3-6x^3+4x^2-21x^2+14x-6x+4 $$

Combine like terms:

$$ 9x^4 \color{blue}{-6x^3} \color{blue}{-6x^3} + \color{red}{4x^2} \color{red}{-21x^2} + \color{green}{14x} \color{green}{-6x} +4 = 9x^4 \color{blue}{-12x^3} \color{red}{-17x^2} + \color{green}{8x} +4 $$