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

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Solution

( $x^{3}$ - 3 $x^{2}$ - x)( $x^{2}$ - 3x + 1)
⇒ x³( $x^{2}$ - 3x + 1) - 3x²( $x^{2}$ - 3x + 1) -x( $x^{2}$ - 3x + 1)
⇒ $x^{5}$ - 3 $x^{4}$ + $x^{3}$ - 3 $x^{4}$ + 9 $x^{3}$ - 3 $x^{2}$ - $x^{3}$ + 3 $x^{2}$ - x
⇒ $x^{5}$ - 6 $x^{4}$ + 9 $x^{3}$ - x

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