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

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

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

Combine like terms:

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

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

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

Combine like terms:

$$ x^2 \color{blue}{-2x} + \color{red}{1} \color{blue}{-3x} + \color{green}{3} + \color{green}{1} = x^2 \color{blue}{-5x} + \color{green}{5} $$

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

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

Combine like terms:

$$ x^5 \color{blue}{-5x^4} + \color{red}{5x^3} \color{blue}{-3x^4} + \color{green}{15x^3} \color{orange}{-15x^2} + \color{green}{2x^3} \color{orange}{-10x^2} +10x = \\ = x^5 \color{blue}{-8x^4} + \color{green}{22x^3} \color{orange}{-25x^2} +10x $$