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Math Help - factorisation problem

  1. #1
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    factorisation problem

    Factorise

    b2c+c2a+a2b-bc2-ca2-ab2

    Deduce from the factors that changing the values of a, b and c to a+x, b+x and c+x respectively, does not alter the value of the expression.
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  2. #2
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    Re: factorisation problem

    b^2 c+c^2 a+a^2 b-bc^2-ca^2-ab^2
    = 〖( b〗^2 c -ab^2)+〖(c〗^2 a- ca^2)+(a^2 b-bc^2)
    = 〖 b〗^2 (c -a)+ac( c- a)+b(a^2-c^2)
    = 〖 b〗^2 (c -a)+ac( c- a)- b(c^2- a^2)
    = 〖 b〗^2 (c -a)+ac( c- a)- b(c+ a)(c-a)
    =( c-a) [〖 b〗^2 +ac- b(c+ a)]
    =( c-a) [〖 b〗^2 +ac- bc-ba]
    = ( c-a) [〖 (b〗^2 -ba)+(ac- bc)]
    =( c-a) [b(b-a)-c(b- a)]
    = ( c-a) (b-a)(b-c)
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  3. #3
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    Re: factorisation problem

    Thankyou
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