Simplify the expression (x^2-2y)(x^2+2y)(square root(16y^4)+square root (x^8)).

We notice that the product of the 1st and the second
factors returns a difference of two squares:

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

(x^2 - 2y)(x^2 + 2y) = x^4 -
4y^2

We'll manage the terms of the 3rd
factor:

sqrt(16y^4) =
4y^2

sqrt x^8 = x^4

We'll
re-write the product, rearranging the terms of the 3rd
factor:

(x^4 - 4y^2)(x^4 +
4y^2)

We notice that we've get a product that returns a
difference of two squares:

(x^4 - 4y^2)(x^4 + 4y^2) =
(x^4)^2 - (4y^2)^2

We'll multiply the
exponents:

(x^4 - 4y^2)(x^4 + 4y^2) = x^(4*2) -
16*y^(2*2)

(x^4 - 4y^2)(x^4 + 4y^2) = x^8 -
16y^4

The requested simplified expression is
x^8 - 16y^4.