Find the continued products :
(i) $(x + 2) (x - 2) (x^{2} - 4)$
(ii) $(2 x - 1) (2 x + 1) (4 x^{2} + 1)$
(iii) $(a x + b) (a x - b) (a^{2} x^{2} + b^{2})$
(iv) $(x + \frac{1}{x}) (x - \frac{1}{x}) (x^{2} + \frac{1}{x^{2}})$

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Solution

$1) (x + 2) (x - 2) (x^{2} - 4)$
$= (x^{2} - 4) (x^{2} - 4)$
$= x^{4} + 16 - 8 x^{2}$

$2) (2 x - 1) (2 x + 1) (4 x^{2} + 1)$
$= (4 x^{2} - 1) (4 x^{2} + 1)$
$= 16 x^{4} - 1$

$3) (a x + b) (a x - b) (a^{2} x^{2} + b^{2})$
$= (a^{2} x^{2} - b^{2}) (a^{2} x^{2} + b^{2})$
$= a^{4} x^{4} - b^{4}$

$4) (x + \frac{1}{x}) (x - \frac{1}{x}) (x^{2} + \frac{1}{x^{2}})$

$= (x^{2} - \frac{1}{x^{2}}) (x^{2} + \frac{1}{x^{2}})$

$= x^{4} - \frac{1}{x^{4}}$

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Similar questions

(i) (x + 2) (x - 2) (x^{2} - 4)

(a x + b) (a x - b) (a^{2} x^{2} + b^{2})

(x - \frac{1}{x}) (x + \frac{1}{x}) (x^{2} - \frac{1}{x^{2}})

(x - \frac{1}{x}) (x + \frac{1}{x}) (x^{2} + \frac{1}{x^{2}}) (x^{4} + \frac{1}{x^{4}})

(2 x + y) (2 x - y) (4 x^{2} + y^{2})

p (x)

g (x)

q (x)

r (x)

p (x)

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

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