If |a| , = a and |b| , = b, then ( a a^2 - b b^2 )^2 =

MCQ

If $|a|\, = a$ and $|b|\, = b,$ then ${\left( {\frac{a}{{{a^2}}} - \frac{b}{{{b^2}}}} \right)^2} = $

A
${\left( {\frac{{a + b}}{{ab}}} \right)^2}$
B
$\frac{{{{(a - b)}^2}}}{{ab}}$
✓
${\left( {\frac{{a - b}}{{ab}}} \right)^2}$
D
$\frac{{{{(a + b)}^2}}}{{ab}}$

✓

Answer

Correct option: C.

${\left( {\frac{{a - b}}{{ab}}} \right)^2}$

c
(c) ${\left( {\frac{a}{{{a^2}}} - \frac{b}{{{b^2}}}} \right)^2} = \frac{{{a^2}}}{{{a^4}}} + \frac{{{b^2}}}{{{b^4}}} - \frac{{2a\,.\,b}}{{{a^2}{b^2}}}$,{$\because $ $a^2 = a^2$ etc.}

$ = \frac{{{a^2} + {b^2} - 2a\,.\,b}}{{{a^2}{b^2}}} = {\left( {\frac{{a - b}}{{ab}}} \right)^2}.$

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