Simplify : ( x - 6 )( x - 4 )( x - 2 ) - Vidyadip

Question

Simplify : $( x - 6 )( x - 4 )( x - 2 )$

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Answer

Using identity :
$(x + a)(x + b)(x + c) = x^3+ (a + b + c)x^2+ (ab+bc+ ca)x +abc$
$( x - 6 )( x - 4 )( x - 2 )$
$= x^3+ (-6 - 4 - 2)x^2 + [-6 \times (-4) + (-4) \times (-2) + (-2) \times (-6)]x + (-6) \times (-4) \times (-2)$
$= x^3- 12x^2+ (24 + 8 + 12)x - 48$
$= x^3- 12x^2 + 44x - 48$

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