Chapter 9 - Section 9.2 - The Dot Product - 9.2 Exercises - Page 646: 42

See proof below

The question asks to prove the given property Given $(u - v) * (u+v) = |u|^2 - |v|^2$ (* means the dot product) $= u * (u-v) + v * (u-v)$ $= u^2 - u * v + v*u - v^2$ $= u^2 - 2 u * v - v^2$ $=|u|^2 - |v|^2$