Question

If p + q =r, then
p^3 + q^3+3pqr = ?
(a) r^3
(b)r^2p
(c) 0
(d) None of these
​

Answer 1

OPTION A → r³

Step-by-step explanation:

• p + q = r

p³ + q³ + 3pqr

• a³ + b³ = (a + b)(a² – ab + b²)

(p + q)(p² – pq + q²) + 3pqr

r (p² + q² – pq ) + 3pqr

• a² + b² = (a + b)² - 2ab

r ( (p + q)² - 2pq – pq ) + 3pqr

r ( r² - 3pq ) + 3pqr

r³ - 3pqr + 3pqr

r³