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Maths-

General

Easy

Question

$left square bracket left parenthesis a cross times b right parenthesis cross times left parenthesis b cross times c right parenthesis left parenthesis b cross times c right parenthesis cross times left parenthesis c cross times a right parenthesis left parenthesis c cross times a right parenthesis cross times left parenthesis a cross times b right parenthesis right square bracket equals$

$[a b c]^{2}$
$[a b c]^{3}$
$[a b c]^{4}$
None of these

The correct answer is: $left square bracket a b c right square bracket to the power of 4 end exponent$

We have $left parenthesis a cross times b right parenthesis cross times left parenthesis b cross times c right parenthesis equals left parenthesis left parenthesis a cross times b right parenthesis. c right parenthesis b minus left parenthesis left parenthesis a cross times b right parenthesis. b right parenthesis c equals left square bracket a b c right square bracket b$
$left parenthesis b cross times c right parenthesis cross times left parenthesis c cross times a right parenthesis equals left parenthesis left parenthesis b cross times c right parenthesis. a right parenthesis c minus left parenthesis left parenthesis b cross times c right parenthesis. c right parenthesis a equals left square bracket b c a right square bracket c$
$left parenthesis c cross times a right parenthesis cross times left parenthesis a cross times b right parenthesis equals left parenthesis left parenthesis c cross times a right parenthesis. b right parenthesis a minus left parenthesis left parenthesis c cross times a right parenthesis. a right parenthesis b equals left square bracket c a b right square bracket a$
$therefore left square bracket left parenthesis a cross times b right parenthesis cross times left parenthesis b cross times c right parenthesis left parenthesis b cross times c right parenthesis cross times left parenthesis c cross times a right parenthesis left parenthesis c cross times a right parenthesis cross times left parenthesis a cross times b right parenthesis right square bracket$
$equals left square bracket left square bracket a b c right square bracket a left square bracket a b c right square bracket b left square bracket a b c right square bracket c right square bracket equals left square bracket a b c right square bracket to the power of 3 end exponent left square bracket a b c right square bracket equals left square bracket a b c right square bracket to the power of 4 end exponent.$

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