The coefficient of x7 in the expansion of (1-x-x3+x4)8 is

Question

The coefficient of x7 in the expansion of (1-x-x3+x4)8 is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(1-x-x3+x4)8=(1-x)8(1-x3)8 =(1- 8 C1 x+ 8 C2 x2- 8 C2 x3+ ldots) (1- 8 C1 x3+ 8 C2 x6- 8 C3 x9+ ldots) ∴ Coefficient of x7 =- 8 C7- 8 C1 × 8 C4- 8 C1 × 8 C2 =-792

Q. The coefficient of x7 in the expansion of (1−x−x3+x4)8 is____

(1−x−x3+x4)8=(1−x)8(1−x3)8 =(1−8C1​x+8C2​x2−8C2​x3+…) (1−8C1​x3+8C2​x6−8C3​x9+…) ∴ Coefficient of x7 =−8C7​−8C1​×8C4​−8C1​×8C2​ =−792

Q. The coefficient of $x^{7}$ in the expansion of $(1 - x - x^{3} + x^{4})^{8}$ is____