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Question Number 7008 by Tawakalitu. last updated on 05/Aug/16
Factorize: (a − b)^5 + (b − c)^5 + (c− a)^5
Factorize:(a−b)5+(b−c)5+(c−a)5
Commented by Yozzii last updated on 05/Aug/16
(a−b), (b−c) and (c−a) are factors since the expression above reduces to zero if a=b, or b=c or c=a. ⇒(a−b)^5 +(b−c)^5 +(c−a)^5 =(a−b)(b−c)(c−a)f(a,b,c) where f(a,b,c) is an expression in a,b and c.
(a−b),(b−c)and(c−a)arefactorssincetheexpressionabovereducestozeroifa=b,orb=corc=a.⇒(a−b)5+(b−c)5+(c−a)5=(a−b)(b−c)(c−a)f(a,b,c)wheref(a,b,c)isanexpressionina,bandc.
Commented by sou1618 last updated on 06/Aug/16
(a−b)^5 +(b−c)^5 +(c−a)^5 =(5/2)(a−b)(b−c)(c−a){(a−b)^2 +(b−c)^2 +(c−a)^2 }
(a−b)5+(b−c)5+(c−a)5=52(a−b)(b−c)(c−a){(a−b)2+(b−c)2+(c−a)2}
Commented by Tawakalitu. last updated on 06/Aug/16
Thanks very much
Thanksverymuch
Answered by Yozzii last updated on 09/Aug/16
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