2C. Prove that, for arbitrary short exact sequences
$0 \to A \xrightarrow{\alpha} P \to X \to 0$, $0 \to B \xrightarrow{\beta} Q \to Y \to 0$
of modules over $R$ with projective modules $P$ and $Q$, we have
$\text{Tor}_n(X, Y) \approx \text{Tor}_{n-2}(A, B)$
for every $n > 2$ and
$\text{Tor}_2(X, Y) \approx \text{Ker}(\alpha \otimes \beta)$.
