Subtract $4 m^{2} + 16 n^{2} - 16 m n$ from $9 m^{2} - 9 n^{2} + 18 m n$

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Solution

To Subtract $4 m^{2} + 16 n^{2} - 16 m n$ from $9 m^{2} - 9 n^{2} + 18 m n$
Consider $4 m^{2} + 16 n^{2} - 16 m n$ and $9 m^{2} - 9 n^{2} + 18 m n$
Subtraction $= 9 m^{2} - 9 n^{2} + 18 m n - (4 m^{2} + 16 n^{2} - 16 m n)$
$= 9 m^{2} - 9 n^{2} + 18 m n - 4 m^{2} - 16 n^{2} + 16 m n = (9 m^{2} - 4 m^{2}) - (9 n^{2} + 16 n^{2}) + (18 m n + 16 m n) = 5 m^{2} - 25 n^{2} + 34 m n$
Hence, subtract $4 m^{2} + 16 n^{2} - 16 m n$ from $9 m^{2} - 9 n^{2} + 18 m n$ is $5 m^{2} - 25 n^{2} + 34 m n$

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