Find $ \left(x-3\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}{ 3 }$.

$$ \begin{aligned}\left(x-3\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3 + \color{red}{3^2} = x^2-6x+9\end{aligned} $$

Multiply each term of $ \left( \color{blue}{x^2-2}\right) $ by each term in $ \left( x^2-6x+9\right) $.

$$ \left( \color{blue}{x^2-2}\right) \cdot \left( x^2-6x+9\right) = x^4-6x^3+9x^2-2x^2+12x-18 $$

Combine like terms:

$$ x^4-6x^3+ \color{blue}{9x^2} \color{blue}{-2x^2} +12x-18 = x^4-6x^3+ \color{blue}{7x^2} +12x-18 $$

Multiply each term of $ \left( \color{blue}{x^4-6x^3+7x^2+12x-18}\right) $ by each term in $ \left( x^3-1\right) $.

$$ \left( \color{blue}{x^4-6x^3+7x^2+12x-18}\right) \cdot \left( x^3-1\right) = x^7-x^4-6x^6+6x^3+7x^5-7x^2+12x^4-12x-18x^3+18 $$

Combine like terms:

$$ x^7 \color{blue}{-x^4} -6x^6+ \color{red}{6x^3} +7x^5-7x^2+ \color{blue}{12x^4} -12x \color{red}{-18x^3} +18 = x^7-6x^6+7x^5+ \color{blue}{11x^4} \color{red}{-12x^3} -7x^2-12x+18 $$