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Without expanding show that |b^2c^2b ...

Without expanding show that `|b^2c^2b c b+cc^2a^2c a c+a a^2b^2a b a+b|=0` .

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$$ \text { L.H.S. }=\left|\begin{array}{ccc} b+c & b c & b^{2} c^{2} \\ c+a & c a & c^{2} a^{2} \\ a+b & a b & a^{2} b^{2} \end{array}\right| $$ Taking bc, ca, ab common from `R_{1}, R_{2}, R_{3}` respectively, we get ...
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