Linear Algebra: Dot Product and Orthogonality

[mateomy]

This is from my homework, I was moving along nicely until I hit this problem, (there's another just like it right after this). I can't find reference for solving this in the chapter I am looking at. The answer is in the back of the book….-2911. Can someone explain this to me?$$||\mathbf{u}|| = 5\, and\: ||\mathbf{v}|| = 7; \,find\: (3\mathbf{u} - 8\mathbf{v}) \circ (3\mathbf{u} + 8\mathbf{v}).$$I know that $||\mathbf{u}||$ is just the length of the vector, etc. I just don't know where to go from there.

 

[lanedance]

try expanding the dot product using its linear properties, should simplify a heap

 

[mateomy]

You were right. Solved it first go after that. Thank you.