Question

!!! Use the sum of cubes identity to find the factors of the expression 8x^6 + 27y^3. Write your answer in the form of the expression on the right of the sum of cubes identity. CLIP IN QUESTION

Answer 1

Answer: Edmentum/plato

Explanation:

Answer 2

(2x² + 3y)(4
`x^(4)` - 6x²y + 9y²)

Explanation:

A sum of cubes is factored in general as

a³ + b³ = (a + b)(a² - ab + b²) , thus

8
`x^(6)` + 27y³

= (2x²)³ + (3y)³ with a = 2x² and b = 3y

= (2x² + 3y)((2x²)² - 2x²(3y) + (3y)²)

= (2x² + 3y)(4
`x^(4)` - 6x²y + 9y²)