Simplify the following expression:
$(4 m + 5 n)^{2} + (5 m + 4 n)^{2}$

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Solution

$\begin{matrix} (4 m + 5 n)^{2} + (5 m + 4 n)^{2} & = 16 m^{2} + 25 n^{2} + 40 m n + 25 m^{2} + 16 n^{2} + 40 m n = 41 m^{2} + 41 n^{2} + 80 m n = 40 (m^{2} + n^{2} + 2 m n) + m^{2} + n^{2} = 40 (m + n)^{2} + m^{2} + n^{2} \end{matrix}$

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

(25 m^{2} - 4 n^{2}) \div (5 m + 2 n)

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