Language Proof and Logic Exercise 36 On Fitch Proofs

Question

Premise 1: A v B

Premise 2: A v C

Goal: A v (B and C)

I'm having a very difficult time figuring out how to get the goal. Please explain step-by-step as to how I do so. Thank you.

Here are the directions from my professor: No Taut Con on this one.You will need to use  -Elim (argument by cases) as your main strategy. However, in the second subproof of your main strategy you'll need to use 

-Elim again (so you'll have nested subproofs).

Answer 1

Given Premise:

#1) A or B

#2) A or C

If a is FALSE, then B must be true, per given premise #1;

If a is False, then C must be true, per given premise #2;

Then B and C MUST hold true...

Therefore, A or (B and C)

If a is true then A or (B and C) must hold true

for any B and C