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Using properties of determinants prove that:

Question:

Using properties of determinants prove that:

$\left|\begin{array}{ccc}(b+c)^{2} & a b & c a \\ a b & (a+c)^{2} & b c \\ a c & b c & (a+b)^{2}\end{array}\right|=2 a b c(a+b+c)^{3}$

Solution:

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