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Simplification of an Expression

Simplify: x-...

Question

Simplify: $(x - 2) (x - 3) (x - 4)$

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Solution

given, $(x - 2) (x - 3) (x - 4)$

$= (x - 2) [x (x - 4) - 3 (x - 4)]$

$= (x - 2) [x^{2} - 4 x - 3 x + 12]$

$= (x - 2) (x^{2} - 7 x + 12)$

$= x (x^{2} - 7 x + 12) - 2 (x^{2} - 7 x + 12)$

$= x^{3} - 7 x^{2} + 12 x - 2 x^{2} + 14 x - 24$

$= x^{3} - 9 x^{2} + 26 x - 24$

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