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

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

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

Combine like terms:

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

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

$$ \left( \color{blue}{2x^4-4x^2+2}\right) \cdot \left( 3x-1\right) = 6x^5-2x^4-12x^3+4x^2+6x-2 $$