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

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

Combine like terms:

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

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

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

Combine like terms:

$$ 4x^3 \color{blue}{-10x^2} + \color{blue}{2x^2} \color{red}{-5x} \color{red}{-12x} +30 = 4x^3 \color{blue}{-8x^2} \color{red}{-17x} +30 $$

Multiply each term of $ \left( \color{blue}{4x^3-8x^2-17x+30}\right) $ by each term in $ \left( x+1\right) $.

$$ \left( \color{blue}{4x^3-8x^2-17x+30}\right) \cdot \left( x+1\right) = 4x^4+4x^3-8x^3-8x^2-17x^2-17x+30x+30 $$

Combine like terms:

$$ 4x^4+ \color{blue}{4x^3} \color{blue}{-8x^3} \color{red}{-8x^2} \color{red}{-17x^2} \color{green}{-17x} + \color{green}{30x} +30 = 4x^4 \color{blue}{-4x^3} \color{red}{-25x^2} + \color{green}{13x} +30 $$