Using properties of determinants prove that: P \[ \left|\begin{arra...

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Using properties of determinants prove that:
P
\[
\left|\begin{array}{ccc}
(b+c)^{2} & a b & c a \\
a b & (a+c)^{2} & b c \\
a c & b c & (a+b)^{2}
\end{array}\right|=2 a b c(a+b+c)^{3} .
\]
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