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 }$.

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

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^2-2x+1}\right) $ by each term in $ \left( x^2+2x+1\right) $.

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

Combine like terms:

$$ x^4+ \, \color{blue}{ \cancel{2x^3}} \,+ \color{green}{x^2} \, \color{blue}{ -\cancel{2x^3}} \, \color{orange}{-4x^2} \, \color{blue}{ -\cancel{2x}} \,+ \color{orange}{x^2} + \, \color{blue}{ \cancel{2x}} \,+1 = x^4 \color{orange}{-2x^2} +1 $$

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

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

Multiply each term of $ \left( \color{blue}{x^5-2x^4-2x^3+4x^2+x-2}\right) $ by each term in $ \left( x+2\right) $.

$$ \left( \color{blue}{x^5-2x^4-2x^3+4x^2+x-2}\right) \cdot \left( x+2\right) = \\ = x^6+ \cancel{2x^5} -\cancel{2x^5}-4x^4-2x^4 -\cancel{4x^3}+ \cancel{4x^3}+8x^2+x^2+ \cancel{2x} -\cancel{2x}-4 $$

Combine like terms:

$$ x^6+ \, \color{blue}{ \cancel{2x^5}} \, \, \color{blue}{ -\cancel{2x^5}} \, \color{green}{-4x^4} \color{green}{-2x^4} \, \color{orange}{ -\cancel{4x^3}} \,+ \, \color{orange}{ \cancel{4x^3}} \,+ \color{red}{8x^2} + \color{red}{x^2} + \, \color{green}{ \cancel{2x}} \, \, \color{green}{ -\cancel{2x}} \,-4 = x^6 \color{green}{-6x^4} + \color{red}{9x^2} -4 $$