If m is the successor of n, find the value of ${(n + m)}^{2}$ , where both n, m are positive integers.

4 n^{2} + 4 n - 1

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4 n^{2} - 4 n + 1

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4 n^{2} + 4 n + 1

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4 n^{2} - 4 n - 1

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Solution

The correct option is C $4 n^{2} + 4 n + 1$
Given that n and m are positive integers
and m is successor of n so
m= n+1
lets apply the identity, ${(n + m)}^{2} = {(n + n + 1)}^{2} = {(2 n + 1)}^{2} = 4 n^{2} + 1 + 4 n Hence, option B is the correct answer .$

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