#10;(4m+5n)^2+(5m+4n)^2 #10; #10; #10;=( 4m )^2+( 5n )^2+2× 4m× #10;5n+( 5m )^2+( 4n )^2+2× 5m× 4n #10; #10; #10;=16m^2+25n^2+40mn+25m^ ...

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Sum of n Terms

Solve 4m+5n...

Question

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

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Solution

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

$= {(4 m)}^{2} + {(5 n)}^{2} + 2 \times 4 m \times 5 n + {(5 m)}^{2} + {(4 n)}^{2} + 2 \times 5 m \times 4 n$

$= 16 m^{2} + 25 n^{2} + 40 m n + 25 m^{2} + 16 n^{2} + 40 m n$

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

Hence , this is the answer.

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

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

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