How would you factor and simplify the following: 6x^2(x^2 – 4)^2 – 5(x^2 – 4)^3

We are asked to factor and simplify 6x^2(x^2-4)^2-5(x^2-4)^3 :
First we factor out the common factor (x^2-4)^2 to get:
(x^2-4)^2(6x^2-5(x^2-4))
Working within the parentheses, we use the distributive property to get:
(x^2-4)^2(6x^2-5x^2+20)
(x^2-4)^2(x^2+20)
Now, x^2-4 is a difference of two squares and will factor further. On the other hand, x^2+20 is prime (irreducible) (at least in the real numbers*). Factoring, we get:
((x+2)(x-2))^2(x^2+20) or
(x+2)^2(x-2)^2(x^2+20) which is the result we seek.
* In the complex numbers, this further factors to:
(x+2)^2(x-2)^2(x+2sqrt(5)i)(x-2sqrt(5)i)
http://mathworld.wolfram.com/PolynomialFactorization.html