If \( \left|\begin{array}{ccc}y+z & x & y \\ z+x & z & x \\ x+y & y & z\end{array}\right|=k(x+y+...

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If \( \left|\begin{array}{ccc}y+z & x & y \\ z+x & z & x \\ x+y & y & z\end{array}\right|=k(x+y+z)(x-z)^{2} \), then \( k= \)
P
W
(1) \( 2 x y z \)
(2) 1
(3) \( x y z \)
(4) \( x^{2} y^{2} z^{2} \)
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