Solution: ∵ Let x=0, and you can get the term without x in the (1+ax+by) n expansion.

∫( 1+AX+BY)n The sum of the absolute values of the coefficients of the terms without X in the expansion is 243.

∴ (1+by) n The sum of absolute values of expansion coefficients is 243 = 3 5.

When y= 1, the sum of the coefficients of the expansion of (1+by) n is (1+b) n.

b≠0

If b > 0, the sum of the absolute values of the coefficients of the expansion with (1+by) n = 3 is 5 = (1+b) n,

∴b=2,n=5

If b < 0, the sum of the absolute values of the coefficients of the expansion with (1+by) n = 3 is 5 = (1-b) n,

∴b=-2,n=5

∵ Let y=0, and you can get the term without y in the expansion of (1+ax+by) n.

∫( 1+AX+BY)n The sum of the absolute values of the coefficients of the terms without Y in the expansion is 32 = 2 5.

∴ (1+AX) n The sum of the absolute values of the expansion coefficients is 32 = 2 5.

When x= 1, the sum of the coefficients of the expansion of (1+ax) n is (1+a) n.

Obviously, a≠0

(1) If a > 0, the sum of the absolute values of the coefficients of the expansion with (1+ax) n = 2 is 5 = (1+a) n,

∴a= 1,n=5

(2) If a < 0, the sum of the absolute values of the coefficients of the expansion of (1+ax) n = 2 5 = (1-a) n,

∴a=- 1,n=5

To sum up, a = 1, b = 2, n=5.

Only d is satisfied.