(i) 64a³ – 27b³ – 144a²b + 108ab²

The expression, 64a³–27b³–144a²b+108ab²can be written as (4a)³–(3b)³–3(4a)²(3b)+3(4a)(3b)²

64a³ – 27b³ – 144a²b + 108ab² =
(4a)³–(3b)³ – 3(4a)²(3b) + 3(4a)(3b)²

=(4a–3b)³

=(4a–3b)(4a–3b)(4a–3b)

Here, the identity, (x – y)³ = x³ – y³ – 3xy(x – y) is used.

(ii) 7p³– (1/216)−(9/2) p²+(1/4)p

The expression, 27p³–(1/216)−(9/2) p²+(1/4)p

can be written as (3p)³–(1/6)³–3(3p)²(1/6)+3(3p)(1/6)²

27p³–(1/216)−(9/2) p²+(1/4)p =
(3p)³–(1/6)³–3(3p)²(1/6)+3(3p)(1/6)²

= (3p–16)³

= (3p–16)(3p–16)(3p–16)