\( \operatorname{If}\left|\begin{array}{ccc}a^{2} & b^{2} & c^{2} \...

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\( \operatorname{If}\left|\begin{array}{ccc}a^{2} & b^{2} & c^{2} \\ (a+\lambda)^{2} & (b+\lambda)^{2} & (c+\lambda)^{2} \\ (a-\lambda)^{2} & (b-\lambda)^{2} & (c-\lambda)^{2}\end{array}\right|=k \lambda\left|\begin{array}{ccc}a^{2} & b^{2} & c^{2} \\ a & b & c \\ 1 & 1 & 1\end{array}\right| \)
\( \lambda \neq 0 \), then \( k \) is equal to:
(a) \( 4 \lambda a b c \)
(b) \( -4 \lambda a b c \)
(c) \( 4 \lambda^{2} \)
(d) \( -4 \lambda^{2} \)
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