Find the fourth term of (a-2b^2) ^4

I would first find (a - 2b^2) ^2

a^2 - 4ab^2 + 4b^4

Then the problem becomes (a^2 - 4ab^2 + 4b^4) (a^2 - 4ab^2 + 4b^4)

Distribute the first over the second

a^4 - 4a^3b^2 + 4ab^4 - 4a^3b^2 + 16a^3b^4 - 16ab^6 + 4a^2b^4 - 16ab^6 + 16b^8

Simplify

a^4 - 8a^3b^2 + 4ab^4 + 16a^3b^4 - 32ab^6 + 4a^2b^4 + 16b^8

rearrange

a^4 - 8a^3b^2 + 16a^3b^4 + 4a^2b^4 + 4ab^4 - 32ab^6 + 16b^8

So the fourth term would be 4a^2b^4 (unless I made an error up there!)