For a Borel function ${psi}:mathbb{R}{ imes}mathbb{R}{ ightarrow}mathbb{R}$ satisfying the functional equation $psi$ (s + t, u + v) + $psi$(s - t, u - v) = $2psi$(s, u) + $2psi$(t, v), we show that it satisfies the functional equation $$psi$$(s, t) = s(s - t)$$psi$$(1, 0) + $$stpsi$$(1, 1) + t(t - s)$$psi$$(0, 1). Using this, we prove the stability of the functional equation f(ax + ay, bz + bw) + f(ax - ay, bz - bw) = 2abf(x, z) + 2abf(y,w) in Banach modules over a unital $C^*$-algebra.