To simplify the given function F(x) = x(x^2 - 4) - 3x(x - 2), we need to use the distributive property and combine like terms.
First, we distribute x in the first term, and we get:
F(x) = x^3 - 4x - 3x^2 + 6x
Next, we can combine like terms:
F(x) = x^3 - 3x^2 + 2x
Therefore, the simplified form of the given function F(x) = x(x^2 - 4) - 3x(x - 2) is F(x) = x^3 - 3x^2 + 2x.