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Purely Imaginary

Simplify the ...

Question

Simplify the following:
$(i) (x + 6) (x + 4) (x - 2)$
$(i i) (x - 6) (x - 4) (x + 2)$
$(i i i) (x + 6) (x - 4) (x - 2)$
$(i v) (x + 6) (x - 4) (x - 2)$

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Solution

(i)(X+6)(X+4)(X-2)
on simplifying $(x + 6) (x^{2} + 2 x - 8)$
$\Rightarrow (x^{3} + 2 x^{2} - 8 x + 6 x^{2} + 12 x - 48)$
$\Rightarrow (x^{3} + 8 x^{2} + 4 x - 48)$
(ii)(x-6)(x-4)(x+2)
on simplifying $(x - 6) (x^{2} - 2 x - 8)$
$\Rightarrow x^{3} - 2 x^{2} - 8 x - 6 x^{2} + 12 x + 48$
$\Rightarrow x^{3} - 8 x^{2} + 4 x + 48$
(iii)(x+6)(x-4)(x-2)
on simplifying $(x + 6) (x^{2} - 6 x + 8)$
$\Rightarrow x^{3} - 6 x^{2} + 8 x + 6 x^{2} - 36 + 48$
$\Rightarrow x^{3} - 28 + 48.$
(iv)(x-6)(x+4)(x-2)
on simplifying
(x-6) $(x^{2} + 2 x - 8)$
$\Rightarrow (x - 6) (x^{2} 2 x - 8)$
$\Rightarrow x^{3} + 2 x^{2} - 8 x - 6 x^{2} - 12 x - 48$
$\Rightarrow x^{3} - 4 x^{2} - 20 x + 48$ .

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Purely Imaginary

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