Sum and Difference of Cubes

Question

Factor Completely: 

216x⁶−125y⁶ =

Answer 1

= (6x^2-5y^2)(36x^4+30x^2y^2+25y^4)

using the general formula

difference of 2 cubes

a^2-b^2 = (a-b)(a^2+ab+b^2)

where a = cube root of 216x^6 = 6x^2

and b = cube root of 125y^6= 5y^2

and if you're not into integer factors or rational coefficients you could go further

to get:

(xsqr6 -ysqr5)(xsqr6+sqr5)(36x^^4 +30x^2y^2 + 25y^2)

but most people wouldn't do that, still it's a possible answer to "completely" factor, depending on what the instructor, textbook or computer program's format is

Answer 2

A³ - B³ = (A - B)(A² + AB + B²)

216x⁶ - 125y⁶ = (6x²)³ - (5y²)³ = (6x² - 5y²)(36x⁴ + 30x²y² + 25y⁴)