Question

Which expression is the completely factored form of x6−64y3 ?

Answer 1

`(x^(2) -4y)(x^(4) +4x^(2) y+16y^(2) )`

is the answer.

Answer 2

We are given this

`x^6 -64y^3`

write it as the difference of cubes

`(x^2)^3 -(4y)^3`

use the formula for the difference of cubes

`(x^2-4y) ((x^2)^2+x^2*4y+(4y)^2)`

Now use the formula for the difference of squares as
`4y = (2√(y) )^2`

`(x-2√(y)) (x+2√(y)) (x^4+4x^2y+16y^2)`