To find the reduced form of the given expression, cos^6(x)sin^6(x)3cos^2(x)sin^2(x), we can start by simplifying each term individually and then combining them.

1. Simplifying cos^6(x):
Using the identity cos^2(x) = 1 - sin^2(x), we can rewrite cos^6(x) as (cos^2(x))^3.
Substituting the identity, we get (1 - sin^2(x))^3.
Expanding this using the binomial theorem, we get:
(1 - sin^2(x))^3 = 1 - 3sin^2(x) + 3(sin^2(x))^2 - (sin^2(x))^3.

2. Simplifying sin^6(x):
Similarly, using the identity sin^2(x) = 1 - cos^2(x), we can rewrite sin^6(x) as (sin^2(x))^3.
Substituting the identity, we get (1 - cos^2(x))^3.
Expanding this using the binomial theorem, we get:
(1 - cos^2(x))^3 = 1 - 3cos^2(x) + 3(cos^2(x))^2 - (cos^2(x))^3.

3. Simplifying 3cos^2(x)sin^2(x):
This can be simplified using the double-angle identity for sine:
sin(2x) = 2sin(x)cos(x).
Therefore, sin^2(x) = (1/2)sin(2x).
Similarly, cos^2(x) = (1/2)cos(2x).
Substituting these values, we get:
3cos^2(x)sin^2(x) = 3(1/2)cos(2x)(1/2)sin(2x) = (3/4)cos(2x)sin(2x).

4. Combining the terms:
Now, substituting the simplified forms of cos^6(x), sin^6(x), and 3cos^2(x)sin^2(x) into the original expression, we get:
(1 - 3sin^2(x) + 3(sin^2(x))^2 - (sin^2(x))^3)(1 - 3cos^2(x) + 3(cos^2(x))^2 - (cos^2(x))^3)((3/4)cos(2x)sin(2x)).
Expanding this expression will result in a long and messy polynomial.

However, notice that there are terms involving sin^3(x) and cos^3(x) in the expression, and these terms will cancel out each other when expanded.
This is because sin^3(x) and cos^3(x) can be expressed in terms of sin(x) and cos(x) using the cube identities:
sin^3(x) = (3sin(x) - sin(3x))/4
cos^3(x) = (3cos(x) + cos(3x))/4.

Therefore, when the expression is expanded, all the terms involving sin^3(x) and cos^3(x) will cancel out, leaving only terms involving sin(x) and cos(x).

Hence, the reduced form of the expression is 1.