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cluponka [151]
2 years ago
9

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

Mathematics
1 answer:
Talja [164]2 years ago
7 0

Answer:

(4x² + 3)(16x^{4} - 12x² + 9)

Step-by-step explanation:

A sum of cubes factors as

a³ + b³ = (a + b)(a² - ab + b²)

64x^{6} = (4x²)³ ⇒ a = 4x²

27 = 3³ ⇒ b = 3

Hence

64x^{6} + 27

(4x² + 3)((4x²)² - (4x² × 3) + 3²)

= (4x² + 3)(16x^{4} - 12x² + 9)

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