Simplify :

$(a b - c)^{2} + 2 a b c$

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Solution

We have, $(a b - c)^{2} + 2 a b c$
[Using the identity, $(x - y)^{2} = x^{2} + y^{2} - 2 x y$ ]
$= (a b)^{2} + c^{2} - (2 \times a b \times c) + 2 a b c$
$= (a b)^{2} + c^{2} - 2 a b c + 2 a b c$
$= a^{2} b^{2} + c^{2}$

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