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

Combine like terms:

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

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

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

Combine like terms:

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

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

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

Combine like terms:

$$ x^4+ \color{blue}{5x^3} \color{blue}{-2x^3} \color{red}{-10x^2} \color{red}{-3x^2} -15x = x^4+ \color{blue}{3x^3} \color{red}{-13x^2} -15x $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 3x^2+3x \right) = -3x^2-3x $$

Combine like terms:

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

Combine like terms:

$$ \color{blue}{-3x^2} \color{red}{-x} +3+x^4+3x^3 \color{blue}{-13x^2} \color{red}{-15x} = x^4+3x^3 \color{blue}{-16x^2} \color{red}{-16x} +3 $$