# Answer to Question #10684 in Algebra for nksprasad

Question #10684

using factor theorem, show that a+b, b+c, c+a are the factors of (a+b+c)^3 - (a^3+b^3+c^3)

Expert's answer

If we consider f(a,b,c)=(a+b+c)^3 - (a^3+b^3+c^3) as a f(a)=(a+b+c)^3 -

(a^3+b^3+c^3) where b,c are parameters, then values a=-b

and a=-c are roots

of equation f(a)=0. So, (a+b) and (a+c) are factors of f(a)=(a+b+c)^3 -

(a^3+b^3+c^3).

Similar consideration f(b)=(a+b+c)^3 - (a^3+b^3+c^3) where

a,c are parameters and b=-c are root of f(b)=0 gives us that (b+c) are

factor

of (a+b+c)^3 - (a^3+b^3+c^3).

(a^3+b^3+c^3) where b,c are parameters, then values a=-b

and a=-c are roots

of equation f(a)=0. So, (a+b) and (a+c) are factors of f(a)=(a+b+c)^3 -

(a^3+b^3+c^3).

Similar consideration f(b)=(a+b+c)^3 - (a^3+b^3+c^3) where

a,c are parameters and b=-c are root of f(b)=0 gives us that (b+c) are

factor

of (a+b+c)^3 - (a^3+b^3+c^3).

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