If $\; \begin{vmatrix} a^{2} & b^{2} & c^{2} \\[0.3em] (a+\lambda)^{2} &(b+\lambda)^{2} & (c+\lambda)^{2} \\[0.3em] (a-\lambda)^{2} & (b-\lambda)^{2} & (c-\lambda)^{2} \\[0.3em] \end{vmatrix}=k \lambda \begin{vmatrix} a^{2} & b^{2} & c^{2} \\[0.3em] a & b& c \\[0.3em] 1 & 1 & 1 \end{vmatrix}\;,\lambda \neq 0\;$ , then k is equal to :

Question

$(a)\;4 \lambda abc\qquad(b)\;-4 \lambda abc\qquad(c)\;4 \lambda^{2} \qquad(d)\;-4 \lambda^{2}$