Question

$Evalute space space open vertical bar table row cell straight b plus straight c end cell straight a straight a row straight b cell space space space space straight c plus straight a end cell straight b row straight c straight c cell space space straight a plus straight b end cell end table close vertical bar$

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Solution

Let space space increment space equals space space open vertical bar table row cell straight b plus straight c end cell straight a straight a row straight b cell space space space space straight c plus straight a end cell straight b row straight c straight c cell space space straight a plus straight b end cell end table close vertical bar space space space space space space space space space space space space space equals space left parenthesis straight b plus straight c right parenthesis space space open vertical bar table row cell straight c plus straight a end cell cell space space straight b end cell row straight c cell space space straight a plus straight b end cell end table close vertical bar space minus straight a space open vertical bar table row straight b cell space space space space space space space space straight b end cell row straight c cell space space space space space straight a plus straight b end cell end table close vertical bar space plus straight a space open vertical bar table row straight b cell space space space straight c plus straight a end cell row straight c straight c end table close vertical bar space space space space space space space space space space space space space equals space left parenthesis straight b plus straight c right parenthesis space space open square brackets table row cell left parenthesis straight c plus straight a right parenthesis left parenthesis straight a plus straight b right parenthesis minus bc end cell end table close square brackets space minus straight a space open square brackets table row cell straight b left parenthesis straight a plus straight b right parenthesis minus bc end cell end table close square brackets space plus straight a space open square brackets table row cell straight b minus straight c left parenthesis straight c plus straight a right parenthesis end cell end table close square brackets space space space space space space space space space space space space equals space left parenthesis straight b plus straight c right parenthesis space left parenthesis ca plus straight a squared space plus ab right parenthesis minus straight a left parenthesis ab plus straight b squared space minus bc right parenthesis space plus straight a space left parenthesis bc minus straight c squared space minus ca right parenthesis space space space space space space space space space space space space equals space abc plus straight a squared space straight b plus ab squared space plus straight c squared space straight a plus straight c space straight a to the power of 2 space end exponent space plus abc plus abc minus ac squared space minus ca squared space space space space space space space space space space space space equals space 4 abc

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