factor and simplify: cos^2 - sin^2cos^2x?

cos^2x - sin^2cos^2x = cos^2x(1 - sin^2x) = cos^4x

remember the identity: sin^2 + cos^2 = 1 so then
cos^2 = 1 - sin^2

Hopefully what you mean is :-

cos ² x - sin ² x cos ² x

cos ² x ( 1 - sin ² x )

cos ² x cos ² x

(cos x)^4

cos^2(x) - sin^2(x)cos^2(x)
= cos^2(x)[1 - sin^2(x)]
= cos^2(x)[cos^2(x)]
= cos^4(x)

I assume there's probably a couple more x's in there. Is this what you wanted?

cos^2 x - sin^2 x cos^2 x

If so, you have a common term of cos^2 x. Factoring that out front:
cos^2x (1 - sin^2 x)

But 1 - sin^2 x = cos^2 x (this comes from solving the identity cos^2 x + sin^2 x = 1 for cos^2 x). So we get:
cos^2 x cos^2 x

Or:
cos^4 x