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 }$.

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

Combine like terms:

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

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

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

Combine like terms:

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

Combine like terms:

$$ \color{blue}{x^2} + \color{red}{4x} + \color{green}{4} +x^4-4x^3+ \color{blue}{8x^2} \color{red}{-8x} + \color{green}{4} = x^4-4x^3+ \color{blue}{9x^2} \color{red}{-4x} + \color{green}{8} $$