How do you factor #(b−c)^3+(c−a)^3+(a−b)^3#?

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Answer 1 · 2017-04-01T19:00:59

#3(b-c)(c-a)(a-b).#

If we use the following Result, we can immediately factorise the

given Exp.#=3(b-c)(c-a)(a-b).#

Result : #x+y+z=0 rArr x^3+y^3+z^3=3xyz.#

Otherwise, consider the following :

Let, #u=b-c, v=c-a rArr u+v=b-a=-(a-b).#

Now, The Exp.#=u^3+v^3+{-(u+v)}^3,#

#=u^3+v^3-(u+v)^3,#

#=u^3+v^3-{u^3+v^3+3uv(u+v)},#

#=-3uv(u+v)=3uv{-(u+v)},#

#:." The Exp.="3(b-c)(c-a)(a-b).#

Enjoy Maths.!