$$ (-1+x)^4 = (-1+x)^2 \cdot (-1+x)^2 $$

Find $ \left(-1+x\right)^2 $ in two steps.

S1: Change all signs inside bracket.

S2: Apply formula

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

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

$$ \begin{aligned}\left(-1+x\right)^2& \xlongequal{ S1 } \left(1-x\right)^2 \xlongequal{ S2 } \color{blue}{1^2} -2 \cdot 1 \cdot x + \color{red}{x^2} = \\[1 em] & = 1-2x+x^2\end{aligned} $$

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

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

Combine like terms:

$$ 1 \color{blue}{-2x} + \color{red}{x^2} \color{blue}{-2x} + \color{green}{4x^2} \color{orange}{-2x^3} + \color{green}{x^2} \color{orange}{-2x^3} +x^4 = x^4 \color{orange}{-4x^3} + \color{green}{6x^2} \color{blue}{-4x} +1 $$

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

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

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

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

Multiply $ \color{blue}{4} $ by $ \left( x^4-4x^3+6x^2-4x+1\right) $ $$ \color{blue}{4} \cdot \left( x^4-4x^3+6x^2-4x+1\right) = 4x^4-16x^3+24x^2-16x+4 $$Multiply $ \color{blue}{132x} $ by $ \left( -1+x\right) $ $$ \color{blue}{132x} \cdot \left( -1+x\right) = -132x+132x^2 $$Multiply $ \color{blue}{17} $ by $ \left( 1-2x+x^2\right) $ $$ \color{blue}{17} \cdot \left( 1-2x+x^2\right) = 17-34x+17x^2 $$

Combine like terms:

$$ \color{blue}{4x^4} -16x^3+24x^2-16x+4+ \color{blue}{4x^4} = \color{blue}{8x^4} -16x^3+24x^2-16x+4 $$

Multiply each term of $ \left( \color{blue}{-132x+132x^2}\right) $ by each term in $ \left( 2x^2-2x+1\right) $.

$$ \left( \color{blue}{-132x+132x^2}\right) \cdot \left( 2x^2-2x+1\right) = -264x^3+264x^2-132x+264x^4-264x^3+132x^2 $$$$ \left( \color{blue}{17-34x+17x^2}\right) \cdot x^2 = 17x^2-34x^3+17x^4 $$

Combine like terms:

$$ \color{blue}{-264x^3} + \color{red}{264x^2} -132x+264x^4 \color{blue}{-264x^3} + \color{red}{132x^2} = 264x^4 \color{blue}{-528x^3} + \color{red}{396x^2} -132x $$

Combine like terms:

$$ \color{blue}{8x^4} \color{red}{-16x^3} + \color{green}{24x^2} \color{orange}{-16x} +4+ \color{blue}{264x^4} \color{red}{-528x^3} + \color{green}{396x^2} \color{orange}{-132x} = \\ = \color{blue}{272x^4} \color{red}{-544x^3} + \color{green}{420x^2} \color{orange}{-148x} +4 $$

Combine like terms:

$$ \color{blue}{272x^4} \color{red}{-544x^3} + \color{green}{420x^2} -148x+4+ \color{green}{17x^2} \color{red}{-34x^3} + \color{blue}{17x^4} = \\ = \color{blue}{289x^4} \color{red}{-578x^3} + \color{green}{437x^2} -148x+4 $$