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

Step-by-step solution

(1+x)^2=1+2 x+x^2 , (1+x^2 )^3=1+3 x^2+3 x^4+x^6, and (1+x^3 )^4=1+4 x^3+6 x^6+4 x^9+x¹² So, the possible combinations for x¹⁰ are: x x^9, x x^6 x^3, x^2 x^2 x^6, x^4 x^6 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+x^2 )^3 (1+x^3 )^4 is 52 .