Square of Sum of Vectors

Theorem
Let $\mathbf a$ and $\mathbf b$ be vector quantities.

Then:
 * $\paren {\mathbf a + \mathbf b}^2 = \mathbf a^2 + 2 \mathbf a \cdot \mathbf b + \mathbf b^2$

where:
 * $\mathbf a \cdot \mathbf b$ denotes dot product
 * $\mathbf a^2$ denotes the square of $\mathbf a$, that is: $\mathbf a \cdot \mathbf a$.

Also see

 * Dot Product of Sum with Difference of Vectors
 * Square of Sum