Let $0 → A → B → C → 0$ be a short exact sequence of $R$-modules. Prove that for any $R$-module $M$ , there is a short exact sequence $0 → A \oplus M → B \oplus M → C → 0$.
Can anyone please help me with this? I don't even have a clue how to start. Have been staring books for hours and I still don't have a clue.