# Vector Simplification Question

1. Jan 25, 2015

### izchief360

I'm trying to simplify the following expression:

(4u + 3v) ⋅ (4u − 2v) − ll 3u − 4v ll2

And I'm unsure how to proceed.

2. Jan 25, 2015

### Stephen Tashi

Assuming the dot represents the inner product, what formulas do you know that give the properties of the inner product?

3. Jan 25, 2015

### izchief360

Is the inner product equivalent to the dot product? The only relevant formula I know is the that of the dot product, but I am unsure of how to apply order of operations when dealing with vectors.

4. Jan 26, 2015

### Hawkeye18

Yes, the inner product is the dot product (in the case of real spaces). Dot product is a multiplication, so it has a higher order then addition/subtraction, and the same order as multiplication by a scalar.

5. Jan 26, 2015

### Stephen Tashi

6. Jan 26, 2015

### izchief360

Thanks folks, I solved it. The process included taking the inside terms of the entire first term and dotting them with the entire second term as follows:
(4u + 3v) ⋅ (4u − 2v)
[4u ⋅ (4u − 2v)] + [3v ⋅ (4u − 2v)]
16u2 - 8u⋅v + 12u⋅v - 6v2

and for the second part, ll 3u − 4v ll2 is equivalent to (3u - 4v)⋅(3u - 4v), and it's the same process as above. Then, just combine like terms.