Prove A → (A ∧ B) ∨ (A ∧ ¬B) using classical logic

Question

I've tried to do this by assuming A, then using the law of excluded middle to get B ∨ ¬B. From here I plan on using or elimination to get A ∧ B then or introduction to get (A ∧ B) ∨ (A ∧ ¬B). I can get a proof of B → A ∧ B but not a proof of ¬B → A ∧ B. Is it possible to get a proof of ¬B → A ∧ B from what I have or do I need to prove A → (A ∧ B) ∨ (A ∧ ¬B) a different way? Thank you.