Given the vectors u-v=3i+2j and u+v=2i+3j, what is the difference u^2-v^2?

Since u^2  - v^2 is the difference of 2 squares, we'll use
the identity:

u^2 - v^2 = (u - v)(u +
v)

We'll have, form enunciation, u-v =3i+2j and
u+v=2i+3j.

(u - v)(u + v) =
(3i+2j)(2i+3j)

We'll remove the
brackets:

(3i+2j)(2i+3j) = 6i^2 + 9i*j + 4i*j +
6j^2

We know that i^2 = 1 and j^2 = 1 , i*j =
0.

(3i+2j)(2i+3j) = 6 + 6 =
12

The value of the difference of 2 squares
is u^2 - v^2 = 12.