Question

Explain how to use a polynomial identity to factor x^6-27y^3

Answer 1

Dont really no sorry

Answer 2

This is a sum of cubes:

x⁶ - 27y³ = (x²)³ + (-3y)³

Recall that

a³ + b³ = (a + b) (a² - ab + b²)

So we have

x⁶ - 27y³ = (x² - 3y) ((x²)² - x² (-3y) + (-3y)²)

x⁶ - 27y³ = (x² - 3y) (x⁴ + 3x²y + 9y²)