Simplify :
$(4 m + 5 n)^{2} + (5 m + 4 n)^{2}$ .

41 m^{2} + 80 m n + 41 n^{2}

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4 m^{2} - 54 m n + 41 n^{2}

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41 m + 80 m n + 4 n^{2}

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41 m^{2} + 10 m n + 41 n^{2}

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Solution

The correct option is A $41 m^{2} + 80 m n + 41 n^{2}$
Given, $(4 m + 5 n)^{2} + (5 m + 4 n)^{2}$ .

We know, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ .

Then,
$(4 m + 5 n)^{2} + (5 m + 4 n)^{2}$
$= [(4 m)^{2} + 2 (4 m) (5 n) + (5 n)^{2}] + [(5 m)^{2} + 2 (5 m) (4 n) + (4 n)^{2}]$
$= 16 m^{2} + 40 m n + 25 n^{2} + 25 m^{2} + 40 m n + 16 n^{2}$
$= 41 m^{2} + 80 m n + 41 n^{2}$ .

Therefore, option $A$ is correct.

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(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

(4 m + 5 n)^{2} + (5 m + 4 n)^{2}

Simplify:
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