Find $ \left(x-2\right)^2 $ using formula.

$$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$.

$$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$

Find $ \left(x+1\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 1 }$.

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

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

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

Combine like terms:

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

Multiply each term of $ \left( \color{blue}{x^3-x^2-8x+12}\right) $ by each term in $ \left( x^2+2x+1\right) $.

$$ \left( \color{blue}{x^3-x^2-8x+12}\right) \cdot \left( x^2+2x+1\right) = \\ = x^5+2x^4+x^3-x^4-2x^3-x^2-8x^3-16x^2-8x+12x^2+24x+12 $$

Combine like terms:

$$ x^5+ \color{blue}{2x^4} + \color{red}{x^3} \color{blue}{-x^4} \color{green}{-2x^3} \color{orange}{-x^2} \color{green}{-8x^3} \color{blue}{-16x^2} \color{red}{-8x} + \color{blue}{12x^2} + \color{red}{24x} +12 = \\ = x^5+ \color{blue}{x^4} \color{green}{-9x^3} \color{blue}{-5x^2} + \color{red}{16x} +12 $$