1. A flat, rectangular board is built by gluing together a number of
square pieces of the same size. The board is m squares wide and n
squares long. Using the letters m and n, write expressions for
(b) the total number of 1 × 1 squares with free edges (the number of
1 × 1 squares that are not completely surrounded by other squares);
I just doubled the perimeter 2(m + n) and then subtracted 4 to correct the overcounting.
Teacher says I am missing the point of the problem and should have done
mn - (m - 2)(n - 2) = mn - mn - 2m - 2n + 4
Whats wrong with getting it simpler?
What is the point of the redundant way?