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Among the following, the factors of ${(l + m)}^{2} - 4 l m$ is

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(l + 2 m) (l + 2 m)

(l + m) (l + m)

(l - m) (l - m)

(l - 2 m) (l - 2 m)

answer is C.

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Detailed Solution

\begin{matrix} {(l + m)}^{2} - 4 l m \\ l^{2} + 2 l m + m^{2} - 4 l m (∵ {(a + b)}^{2} = a^{2} + 2 a b + b^{2}) \\ l^{2} + m^{2} - 4 l m + 2 l m \\ l^{2} + m^{2} - 2 l m \\ {(l - m)}^{2} = (l - m) (l - m) (∵ a^{2} + 2 a b + b^{2} = {(a - b)}^{2}) \end{matrix}

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