(a+b)^4
=[(a+b)^2]^2
=[a^2+2ab+b^2]^2
=[a^2+(2ab+b^2)]^2
=a^4+2a^2(2ab+b^2)+(2ab+b^2)^2
=a^4+4a^3b+2a^2b^2+4a^2b^2+4ab^3+b^4
=a^4+4a^3b+6a^2b^2+4ab^3+b^4