Using multiplication properties calculate (a-2b)(a^2+4b^2)(a+2b)

First, we'll apply the commutative property for the 2nd
and 3rd factors:

(a^2+4b^2)(a+2b) =
(a+2b)(a^2+4b^2)

We'll re-write the
product:

(a-2b)(a+2b)(a^2+4b^2)

We
notice that the product of the first 2 factors could be replaced by the difference of
squares:

(a^2 -
4b^2)(a^2+4b^2)

This product could be also replaced by its
equivalent difference of squares:

(a^2 - 4b^2)(a^2+4b^2) =
(a^2)^2 - (4b^2)^2

(a^2 - 4b^2)(a^2+4b^2) = a^4 -
16b^4

The result of the product is:
(a-2b)(a^2+4b^2)(a+2b)=a^4 - 16b^4