If the equilibrium constant for A B + C is Keq(1) and that of B + C P is Keq(2), the equilibrium constant for A P is:

Rule: When reactions are added, their equilibrium constants are multiplied.

Step 1 — Add the two reactions: $\mathrm{A \rightleftharpoons B + C} \quad K_{eq}^{(1)} \mathrm{B + C \rightleftharpoons P} \quad K_{eq}^{(2)}$

Adding: $\mathrm{A \rightleftharpoons P}$

Step 2 — Combined equilibrium constant: $K = K_{eq}^{(1)} \times K_{eq}^{(2)}$

This follows from the fact that $K = \frac{[P]}{[A]}$ and: $K_{eq}^{(1)} \times K_{eq}^{(2)} = \frac{[B][C]}{[A]} \times \frac{[P]}{[B][C]} = \frac{[P]}{[A]}$

Answer: Option (4) — $K_{eq}^{(1)} \cdot K_{eq}^{(2)}$