Question

factories r^3(s-t)^3+s^3(t-r)^3+t^3(r-s)^3

please solve properly please do it urgent need please​

Answer 1

let

a =r(s-t)

b = s(t-r)

c=t(r-s)

we can see that a + b + c = 0 (expand and check)

now using the famous identity

(a+b+c)(a²+b²+c²-ab-bc-ca)=a³+b³+c³-3abc

now put a+b+c=0

hence a³+b³+c³=3abc

hence

r³(s-t)³+s³(t-r)³+t³(r-s)³=3rst(r-s)(s-t)(t-r)

that famous identity is actually to be remembered (please expand and check if you don't believe the identity)