Factor: x^9+y^9= (x^3)^3+(y^3)^3....what next?

Sum of perfect cubes:

a³ + b³ = (a + b)(a² – ab + b²)

where a = x³ and b = y³

so the answer is:

x^9 + y^9 = (x³ + y³)(x^6 - x³y³ + y^6)

Seems like an odd problem to do if you haven't learned how to factor sum of cubes:

a³ + b³ = (a+b) (a² − ab + b²)

x⁹ + y⁹

= (x³)³ + (y³)³

= (x³ + y³) ((x³)² − (x³)(y³) + (y³)²)

= (x³ + y³) (x⁶ − x³y³ + y⁶)

= (x + y) (x² − xy + y²) (x⁶ − x³y³ + y⁶)

a³ + b³ = (a+b) (a² - ab + b²)