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Math Help - please help

  1. #1
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    please help

    what will be the ultimate result
    (a+b+c)(-a+b+c)(a-b+c)(a+b-c)
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  2. #2
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    Hello jashansinghal
    Quote Originally Posted by jashansinghal View Post
    what will be the ultimate result
    (a+b+c)(-a+b+c)(a-b+c)(a+b-c)
    If we group the brackets in pairs we can write:

     (a+b+c)(-a+b+c)(a-b+c)(a+b-c)=\Big( (a+b+c)(-a+b+c)\Big)\Big((a-b+c)(a+b-c)\Big)

    =\Big( ([b+c]+a)([b+c]-a)\Big)\Big((a-[b-c])(a+[b-c])\Big)

    =([b+c]^2 - a^2)(a^2 -[b-c]^2)

    =[b+c]^2a^2-([b+c][b-c])^2-a^4+a^2[b-c]^2

    =2a^2b^2+2a^2c^2-(b^2-c^2)^2-a^4

    =2a^2b^2+2a^2c^2+2b^2c^2 -a^4-b^4-c^4

    Grandad
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