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

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

Combine like terms:

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

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

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

Combine like terms:

$$ 2x^3 \color{blue}{-3x^2} + \color{blue}{6x^2} \color{red}{-9x} + \color{red}{4x} -6 = 2x^3+ \color{blue}{3x^2} \color{red}{-5x} -6 $$

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

$$ \left( \color{blue}{2x^3+3x^2-5x-6}\right) \cdot \left( 2x-5\right) = 4x^4-10x^3+6x^3-15x^2-10x^2+25x-12x+30 $$

Combine like terms:

$$ 4x^4 \color{blue}{-10x^3} + \color{blue}{6x^3} \color{red}{-15x^2} \color{red}{-10x^2} + \color{green}{25x} \color{green}{-12x} +30 = 4x^4 \color{blue}{-4x^3} \color{red}{-25x^2} + \color{green}{13x} +30 $$