Difference of cubes?

Question

how to solve x^6-64 using difference of cubes.

The answer is (x-2)(x+2)(x^4+4x^2+16)

thankyou

Answer 1

The formula is a³ - b³ = (a-b)(a²+ab+b²)

 

x⁶ - 64 = (x²)³ - (4)³

 

Substitute into the formula using a = x² and b = 4

 

So, x⁶ - 64 = (x²-4)((x²)²+(x²)(4)+(4)²)

 

                = (x-2)(x+2)(x⁴+4x²+16)