Evaluate the following determinants without expansion as far as possible.
$∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & b c & b c (b + c) 1 & c a & c a (c + a) 1 & a b & a b (a + b) \end{matrix} ∣ ∣ ∣ ∣ ∣$

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Solution

Applying $R_{1}, R_{2}, R_{3}$ by a, b and c respectively and divide by abc. Now take out abc from $C_{3}$ and question reduces to form of Q. Apply $C_{1} + C_{3}$ .

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