Question

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

Answer 1

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 $4y = (2\sqrt{y} )^2$

$(x-2\sqrt{y}) (x+2\sqrt{y}) (x^4+4x^2y+16y^2)$

Answer 2

$(x^{2} -4y)(x^{4} +4x^{2} y+16y^{2} )$

is the answer.