Question

factorise (x-a)³+(x-b)³+(x-c)³ if x+y+z=a+b+c

Answer 1

Given,
x + y + z = a + b + c
x + y + z -a - b - c = 0
(x - a) + ( y -b) + (z - c) = 0
Let (x - a) = P
(y - b) = Q
(z - c) = R
hence, (P + Q + R) = 0

we know ,
P³ + Q³ + R³ = 3PQR when ,
P + Q + R = 0

above you can see that ,
P + Q+ R = 0,
so, P³ + Q³ + R³ = 3PQR
now, put P, Q , and R values
(x - a)³ + (y - b)³ + (z - c)³ = 3(x - a)(y - b)(z - c)