Simplify the following: (2p + 3q)(4p 2 - 6pq + 9q 2 )

(2p + 3q)(4p 2 - 6pq + 9q 2 ) = (2p + 3q)[(2p) 2 - (2p)(3q) + (3q) 2 ] We know that (a + b)(a 2 - ab + b 2 ) = a 3 + b 3 ∴ (2p + 3q)[(2p) 2 - (2p)(3q) + (3q) 2 ] = (2p) 3 + (3q) 3 = 8p 3 + 27q 3