C3 Identify proof question

I have no idea how I have messed up this identity proof question

Prove: Cos4x is identical to 8cos^(4)x-8cos^(2)x+1

I started with the left hand side, rewriting it as

Cos(2x+2x)

I then used the compound formula to obtain

cos2xcos2x-sin2xsin2x

Using double angle formulae

(cos^(2)x-sin^(2)x)^(2) - (2sinxcosx)^2

Expanding the squared brackets to obtain

cos^(4)x-2cos^(2)xsin^(2)x+sin^(4)x+4sin^(2)xcos^(2)x

First error - in red - should be minus.

Not checked the rest.