i'm afraid that method of expansion is incorrect. let's prove it.

try you method of expansion to calculate:

(1 + 2 + 3)(4 + 5)

you will get 120

the correct answer is 54

or even look at the line where you have the expression for (e + f)^3 as e^3f + 2e^2f^2 + ef^3, you kow that's wrong