$\lvert \vec{a} \rvert = 3$ and $\lvert \vec{b} \rvert = 4$. What is $(\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b})$?

Explanation

1. 01

   The cross terms $\vec{a} \cdot \vec{b}$ and $\vec{b} \cdot \vec{a}$ cancel: it is $\lvert \vec{a} \rvert^{2} - \lvert \vec{b} \rvert^{2}$.

2. 02

   $9 - 16 = -7$.