Simplify $(x^{3} - 3 x^{2} - x) (x^{2} - 3 x + 1)$

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Solution

$(x^{3} - 3 x^{2} - x) (x^{2} - 3 x + 1)$

$\Rightarrow$ $x^{3} (x^{2} - 3 x + 1) - 3 x^{2} (x^{2} - 3 x + 1) - x (x^{2} - 3 x + 1)$

$\Rightarrow$ $x^{5} - 3 x^{4} + x^{3} - 3 x^{4} + 9 x^{3} - 3 x^{2} - x^{3} + 3 x^{2} - x$

$\Rightarrow$ $x^{5} - 6 x^{4} + 9 x^{3} - x$

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