factor x^15-y^6z^15

Question

how do you factor x^15-(y)^6(z)^15

Answer 1

This looks like a difference of two cubes, since the exponents (15, 6, and 15) are all divisible by 3.

From this, we can say that

x¹⁵ = (x⁵)³

(y⁶z¹⁵) = (y² z⁵)³

Substituting into our expression, we get (x⁵)³ - (y²z⁵)³

Using the difference of two squares formula, we get

(x⁵ - y²z⁵)[(x⁵)² + (x⁵)(y²z⁵) + (y²z⁵)²] which follows \

(x⁵ - y²z⁵)[x¹⁰ + x⁵y²z⁵ + y⁴z¹⁰]