$space Prove space that space open vertical bar table row cell straight b plus straight c end cell cell space space straight a end cell cell space space straight a end cell row straight b cell space space straight c plus straight a end cell cell space space straight b end cell row straight c cell space straight c end cell cell space space straight a plus straight b end cell end table close vertical bar space equals 4 abc$

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

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