What would (4sqrt(3)-2sqrt(5) be multiplied by to get a product of (4sqrt(3))^3 - (2sqrt(5))^3?

Answer 1

(4√3 - 2√5)(.....) = (4√3)^3 - (2√5)^3

ahh, you should recognize the difference of cubes factoring pattern

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

notice that x corresponds with 4√3
and that y corresponds with 2√5

so what do you think?