Find a ⋅ b a = 7i - 4j, b = 4i + 3j

This is a binomial. You can multiply it out by substituting 7i-4j for a, and 4i+3j for b.

(7i-4j) (4i+3j)

you come up with: 28i^2 + 21ij - 16ij - 12ij

this then comes out to be 28i^2 - 7ij

this is an odd choice of variables for a problem ... let me know if this is the answer you were looking for.