Question

What is 64x^6 + 27 written as a sum of cubes?

Answer 1

(4x² + 3)(16
`x^(4)` - 12x² + 9)

Explanation:

A sum of cubes factors as

a³ + b³ = (a + b)(a² - ab + b²)

64
`x^(6)` = (4x²)³ ⇒ a = 4x²

27 = 3³ ⇒ b = 3

Hence

64
`x^(6)` + 27

(4x² + 3)((4x²)² - (4x² × 3) + 3²)

= (4x² + 3)(16
`x^(4)` - 12x² + 9)