Answer 1

To simplify, we will proceed as follows:

\[\left( 7m - 8n \right)^2 + \left( 7m + 8n \right)^2 \]

\[ = 2 \left( 7m \right)^2 + 2 \left( 8n \right)^2 \left[ \because \left( a - b \right)^2 + \left( a + b \right)^2 = 2 a^2 + 2 b^2 \right]\]

\[ = 98 m^2 + 128 n^2 \]