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)^3 $ using formula

$$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$

where $ A = x $ and $ B = 1 $.

$$ \left(x+1\right)^3 = x^3+3 \cdot x^2 \cdot 1 + 3 \cdot x \cdot 1^2+1^3 = x^3+3x^2+3x+1 $$

Multiply $ \color{blue}{4} $ by $ \left( x-3\right) $ $$ \color{blue}{4} \cdot \left( x-3\right) = 4x-12 $$

Multiply each term of $ \left( \color{blue}{4x-12}\right) $ by each term in $ \left( x^2-2x+1\right) $.

$$ \left( \color{blue}{4x-12}\right) \cdot \left( x^2-2x+1\right) = 4x^3-8x^2+4x-12x^2+24x-12 $$

Combine like terms:

$$ 4x^3 \color{blue}{-8x^2} + \color{red}{4x} \color{blue}{-12x^2} + \color{red}{24x} -12 = 4x^3 \color{blue}{-20x^2} + \color{red}{28x} -12 $$

Multiply each term of $ \left( \color{blue}{4x^3-20x^2+28x-12}\right) $ by each term in $ \left( x^3+3x^2+3x+1\right) $.

$$ \left( \color{blue}{4x^3-20x^2+28x-12}\right) \cdot \left( x^3+3x^2+3x+1\right) = \\ = 4x^6+12x^5+12x^4+4x^3-20x^5-60x^4-60x^3-20x^2+28x^4+84x^3+84x^2+28x-12x^3-36x^2-36x-12 $$

Combine like terms:

$$ 4x^6+ \color{blue}{12x^5} + \color{red}{12x^4} + \color{green}{4x^3} \color{blue}{-20x^5} \color{orange}{-60x^4} \color{blue}{-60x^3} \color{red}{-20x^2} + \color{orange}{28x^4} + \color{green}{84x^3} + \color{orange}{84x^2} + \color{blue}{28x} \color{green}{-12x^3} \color{orange}{-36x^2} \color{blue}{-36x} -12 = \\ = 4x^6 \color{blue}{-8x^5} \color{orange}{-20x^4} + \color{green}{16x^3} + \color{orange}{28x^2} \color{blue}{-8x} -12 $$