Question

if p,q,r are in ap then p3 +r3-8q3 is equal to​

Answer 1

Answer:

-6pqr

Step-by-step explanation:

Since p, q and r in AP

=> q - p = r - q               ( ∵ common difference = tₙ₊₁ - tₙ  is equal )

=> 2q = p + r

Cubing both sides

=> 8q³ = p³  + r³  + 3pr(p + r)         [ ∵ (a+b)³ = a³+b³ + 3ab(a+b) ]

=>  8q³ = p³  + r³  + 3pr(2q)

=> 8q³ = p³  + r³  + 6pqr

=> p³  + r³ - 8q³ = -6pqr