Question

Which one is correct option:

(216p³ - 1/729q³)

1. (6p - 1/9q)(- 36p2 + 2p/3q + 81q2)
2. (6p - 1/9q)(36p² + 2p/3q + 1/81q²)
3. (6p + 1/9q)(36p2 - 2p/3q - 81q2)
4. (6p + 1/9q)(36p2 - 2p/3q + 81q2)

Answer 1

Correct Answer - Option 2 : (6p - 1/9q)(36p² + 2p/3q + 1/81q²)

Formula Used:

(a³ - b³) = (a - b)(a² + ab + b²)

Calculation:

(216p3 - 1/729q3)

(a3 - b3) = (a - b)(a2 + ab + b2)

a³ = 216 = 6 × 6× 6

a = 6

b³ = 1/729 = 1/9 × 1/9 × 1/9

b = 1/9

⇒ [6p - 1/9q][(6p)2 + (6p)(1/9q) + (1/9q)2]

⇒ (6p - 1/9q)(36p2 + 2p/3q + 1/81q2)

∴ (216p3 - 1/729q3) = (6p - 1/9q)(36p2 + 2p/3q + 1/81q2)

The correct option is 2 i.e. (6p - 1/9q)(36p2 + 2p/3q + 1/81q2)