Question

If p, q, r are in A.P., then p^{3} + r^{3} -8q^{3} is

Answer 1

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Since, p,q and r are in AP,

(p+r)/2

p^3 + r^3 - 8q^3

p^3 + r^3 - 8[(p+r)/2]^3

p^3 + r^3 - 8[p^3 + r^3 + 3p2r + 3r2p]/8

p^3 + r^3 - p^3 - r^3 - 3p2r - 3r2p

-[3p2r + 3r2p]

-3pr(p + r)

-3pr(2q) (p+r = 2q)

-6pqr