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