Suppose that u and v are orthogonal vectors in R^n. Find the value of the expression <3u-v. 3u+v>.

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Suppose that u and v are orthogonal vectors in R^n. Find the value of the expression <3u-v. 3u+v>.

Mathematics
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The notation used here "" is the way they represent the dot product of vector x and vector y in my current textbook
you can distribute in the dot product so use FOIL and then bear in mind that \(\mathbf u \bullet \mathbf v = 0 \) and vice versa
if that worries you, start with this idea and expand it out to 4 vectors \[ \mathbf A \cdot ( \mathbf B + \mathbf C ) = \mathbf A \cdot \mathbf B + \mathbf A \cdot \mathbf C .\] now let \(\mathbf A = \mathbf D + \mathbf E \)

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