Find the number of ordered quadruples of positive integers (a,b,c,d ) such that ab +cd =10.

Answer 1

so you have
1+9=10
2+8=10
...
9+1=10

consider 4+6 = 10
to get 4 we have 1x4 , 2x2 , 4x1
to get 6 we have 1x6, 2x3, 3x2, 6x1
so one possible quadruple is (2,2,3,2)

start grinding them out