Find $ \left(1-x\right)^3 $ using formula

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

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

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

Find $ \left(1-4x\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}{ 4x }$.

$$ \begin{aligned}\left(1-4x\right)^2 = \color{blue}{1^2} -2 \cdot 1 \cdot 4x + \color{red}{\left( 4x \right)^2} = 1-8x+16x^2\end{aligned} $$

Multiply each term of $ \left( \color{blue}{1-3x+3x^2-x^3}\right) $ by each term in $ \left( 1-8x+16x^2\right) $.

$$ \left( \color{blue}{1-3x+3x^2-x^3}\right) \cdot \left( 1-8x+16x^2\right) = \\ = 1-8x+16x^2-3x+24x^2-48x^3+3x^2-24x^3+48x^4-x^3+8x^4-16x^5 $$

Combine like terms:

$$ 1 \color{blue}{-8x} + \color{red}{16x^2} \color{blue}{-3x} + \color{green}{24x^2} \color{orange}{-48x^3} + \color{green}{3x^2} \color{blue}{-24x^3} + \color{red}{48x^4} \color{blue}{-x^3} + \color{red}{8x^4} -16x^5 = \\ = -16x^5+ \color{red}{56x^4} \color{blue}{-73x^3} + \color{green}{43x^2} \color{blue}{-11x} +1 $$