Question

Factorise : r³(s - t)³ + s³(t - r)³ + t³(r - s)³…

Answer 1

if a+b+c=0
then a^3 + b^3 + c^3 = 3abc
here a equals to r(s-t)
b equals to s(t-r) and c equals to t(r-s)

as..a^3 + b^3 + c^3 = 3abc
=3rst(s-t)(r-s)(t-r)

Answer 2

r(s-t) + s(t-r) + t(r-s)
=rs -rt +st -sr +tr -ts
=0

∵a+b+c= 0
∴a³+b³+c³ = 3abc

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

=3rst(s-t)(t-r)(r-s)