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

Question

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

Accepted Answer

$$ \because $$ $\,\,\,$$ (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 combination for x10 are :

x . x9,   x . x6.  x3,  x2 . x2 . x6 , x4 . x6

Corresponding coefficients are 2 $$ \times $4, 2$ \times $1$ \times $4, 1$ \times $3$ \times $6,

3$ \times $6   or   8, 8, 18, 18.$\therefore\,\,\,$

Solutions · 1