We are given this
[tex]x^6 -64y^3[/tex]
write it as the difference of cubes
[tex](x^2)^3 -(4y)^3[/tex]
use the formula for the difference of cubes
[tex](x^2-4y) ((x^2)^2+x^2*4y+(4y)^2)[/tex]
Now use the formula for the difference of squares as [tex]4y = (2\sqrt{y} )^2[/tex]
[tex](x-2\sqrt{y}) (x+2\sqrt{y}) (x^4+4x^2y+16y^2)[/tex]
[tex](x^{2} -4y)(x^{4} +4x^{2} y+16y^{2} )[/tex]
is the answer.
