What should be added to $(a^{2} + b^{2})$ so that it becomes equal to $(a - b)^{2}$ ?

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Solution

Let x be the polynomial that needs to be added.
so $(a^{2} + b^{2}) + x = (a - b)^{2}$
$\Rightarrow (a^{2} + b^{2}) + x = a^{2} + b^{2} - 2 a b$
$\Rightarrow x = - 2 a b$ .

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