The coefficient of x10 in the expansion of (1+x)2(1+x2)3(1+x3)4 is equal to :

(1+x)2 = 1 + 2x + x2
(1+x2)3 = 1 + 3x2 + 3x4 + x6
(1+x3)4 = 1 + 4x3 + 6x6 + 4x9 + x12
From the above binomial expansions, we want the terms containing x10 after multiplication.
So, the combinations are:
x2x8, x2x6x2, x4x6, x2x2x6, x1x9
Their coefficients are:
2 x 4 = 8
2 x 3 x 6 = 36
1 x 3 x 6 = 18
1 x 3 x 6 = 18
2 x 4 = 8
Sum of the coefficients is 8 + 8 + 18 + 18 = 52
Hence, the coefficient of x10 in the expansion of (1+x)2(1+x2)3(1+x3)4 is 52