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

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

Combine like terms:

$$ \, \color{blue}{ \cancel{x^4}} \,+ \color{green}{x^5} \color{orange}{-x^3} + \color{green}{x^5} +x^6 \, \color{blue}{ -\cancel{x^4}} \, \color{orange}{-x^3} \, \color{blue}{ -\cancel{x^4}} \,+x^2 = \\ = x^6+ \color{green}{2x^5} \color{blue}{-x^4} \color{orange}{-2x^3} +x^2 $$

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

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

where $ A = x^3 $ and $ B = x $.

$$ \left(x^3-x\right)^3 = \left( x^3 \right)^3-3 \cdot \left( x^3 \right)^2 \cdot x + 3 \cdot x^3 \cdot x^2-x^3 = x^9-3x^7+3x^5-x^3 $$

Multiply $ \color{blue}{3x^2} $ by $ \left( x^3-x\right) $ $$ \color{blue}{3x^2} \cdot \left( x^3-x\right) = 3x^5-3x^3 $$

Combine like terms:

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

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

$$ - \left( x^9-3x^7+3x^5-x^3 \right) = -x^9+3x^7-3x^5+x^3 $$

Combine like terms:

$$ x^6+ \color{blue}{5x^5} -x^4 \color{red}{-5x^3} +x^2-x^9+3x^7 \color{blue}{-3x^5} + \color{red}{x^3} = -x^9+3x^7+x^6+ \color{blue}{2x^5} -x^4 \color{red}{-4x^3} +x^2 $$