Consider two positive even integers less than 15 (not necessarily distinct). When the sum of these two numbers is added to their product, how many different possible values may result?
+128475 [2 +2] + 2*2 = 8 [4 + 4] + 4*4 = 24 [ 6 + 6 ] + 6*6 = 48
[2 + 4] + 2*4 = 14 [4 + 6] + 4*6 = 34 [6 + 8 ] + 6*8 = 62
[2 + 6] + 2*6 = 20 [4 + 8 ] + 4*8 = 44 [ 6 + 10] + 6*10 = 76
[2 + 8] + 2*8 = 26 [4 + 10 ] + 4*10 = 54 [6 + 12] + 6*12 = 90
[2 + 10] + 2*10 = 32 [ 4 + 12] + 4*12 = 64 [6 + 14] + 6 * 14 = 104
[2 + 12] + 2*12 = 38 [4 + 14 ] + 4*14 = 74
[ 2 + 14] + 2*14 = 44
[8 + 8 ] + 8* 8 = 80 [ 10 + 10] + 10*10 = 120 [12 + 12] + 12*12 = 168
[ 8 + 10] + 8*10 = 98 [10 + 12] + 10*12 = 142 [ 12 + 14] + 12*14 = 194
[8 + 12] + 8*12 = 116 [10 + 14] + 10*14 = 164
[8 + 14] + 8*14 = 134
[14 + 14] + 14*14 = 224
Total different values = 7 + 5 + 5 + 4 + 3 + 2 + 1 = 27
