Question

If p q r are in ap prove that (p+2q-r)(2q+rpr+p-q)=4 pqr

Answer 1

hope this will help you

Answer 2

p, q, r are in AP
So
q - p = r - q
Thus
2q = p + r

Now according to question

(p+2q-r) (2q+rpr + p-q)  = (p + p + r -r) (p + r + rpr + p - q)
                                        = (2p) ( 2p + r - q +rpr)
                                       = (2p) (2qr)
                                      = 4 pqr