Completely factor this equation. 8x^3 + y^6?

Question

Please help.

Answer 1

The sum of perfect cubes a and b can be factored.

a³ + b³ = (a + b)(a² - ab + b²)

Let
a = 2x
b = y²

And we have

8x³ + y^6 = (2x)³ + (y²)³ = (2x + y²)(4x² - 2xy² + y^4)

Answer 2

Please recall that 8 = 2^3

So 8x^3 = 2^3 * x^3 = (2x)^3
y^6 can be written = (y^2)^3

So, 8x^3 + y^6 = (2x)^3 + (y^2)^3

(For the later part, see Northstar's answer. I couldn't recall the expansion of a^3 + b^3)

Answer 3

This is an expression, not an equation.
8x^3 + y^6
= (2x)^3 + (y^2)^3
=[2x + y^2]^3 -- 3(2x)(y^2)[2x + y^2]
=[2x + y^2][(2x + y^2)^2 -- 6xy^2]
=(2x + y^2)[4x^2 + 4xy^2 + y^4 -- 6xy^2]
=(2x + y^2)(4x^2 -- 2xy^2 + y^4)