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!!! 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

Use the sum of cubes identity to find the factors of the expression 8x6 27y3 Write your answer in the form of the expression on the right of the sum of cubes i class=

Respuesta :

Answer:

(2x² + 3y)(4[tex]x^{4}[/tex] - 6x²y + 9y²)

Step-by-step explanation:

A sum of cubes is factored in general as

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

8[tex]x^{6}[/tex] + 27y³

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

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

= (2x² + 3y)(4[tex]x^{4}[/tex] - 6x²y + 9y²)

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