Using properties of determinants prove that: \[ \left|\begin{array}{lll} (a+1)(a+2) & a+2 & 1 \\...

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Using properties of determinants prove that:
\[
\left|\begin{array}{lll}
(a+1)(a+2) & a+2 & 1 \\
(a+2)(a+3) & a+3 & 1 \\
(a+3)(a+4) & a+4 & 1
\end{array}\right|=-2
\]
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