∵(1+x)2=1+2x+x2, (1+x2)3=1+3x2+3x4+x6 and (1+x3)4=1+4x3+6x6+4x9+x12 So, the possible combinations for x10 are: x⋅x9,x⋅x6⋅x3,x2⋅x2⋅x6,x4⋅x6 Corresponding coefficients are 2×4,2×1×4,1×3×6,3×6 or 8,8,18,18 ∴ Sum of the coefficient is 8+8+18+18=52 Therefore, the coefficient of x10 in the expansion of (1+x)2(1+x2)3(1+x3)4 is 52.