Question

(2a-b-c)3 + (2b-a-c)3 + (2a-a-b)3

Answer 1

Answer:

3(2a-b-c)(2b-a-c)(2a-a-b)

Step-by-step explanation:

Let,

        2a-b-c = p

        2b-a-c = q

        2a-a-b = r

Therefore, p+q+r = 2a-b-c  +  2a-b-c  +  2a-a-b

                          = 0

  (2a-b-c)3 + (2b-a-c)3 + (2a-a-b)3

= p3 + q3 + r3

= p3 + q3 + r3 - 3pqr + 3pqr

= (p+q+r)(p2 + q2 + r2 - pq - qr - rp) + 3pqr

= 0 (p2 + q2 + r2 - pq - qr - rp) + 3pqr

= 0 + 3pqr

= 3pqr

= 3(2a-b-c)(2b-a-c)(2a-a-b)     Ans