Question

(5a-7b)^3+(7b-9c)^3+(9c-5a)^3​

Answer 1

Answer:

We have,

a3 (b – c)3 + b3 (c – a)3 + c3 (a – b)3

We know that,

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

Also,

If, (x + y + z) = 0

Then (x3 + y3 + z3) = 3xyz

Since,

(5a – 7b) + (9c – 5a) + (7b – 9c) = 5a – 7b + 9c – 5a + 7b – 9c = 0

Therefore,

(5a – 7b)3 + (9c – 5a)3 + (7b – 9c)3 = 3 (5a – 7b) (9c – 5a) (7b – 9c)