The co-efficient of x7 in the expansion of (1 - x4) (1 + x)9 is

Question

The co-efficient of x7 in the expansion of (1 - x4) (1 + x)9 is (A) 27 (B) -24 (C) 48 (D) -48

Tardigrade Admin · Accepted Answer

(1-x4) (1+ 9c1x+ 9c2x2+ 9c3x3+ 9c4x4+ 9c5x5 + 9c6x6+ 9c7x7+ 9c8x8+ 9c9x9 ) Co-eff. of x7 = 9c7- 7c3 = 7c2 - 9c3 = (9×8/1× 2) - (9× 8× 7/1× 2× 3) = 36 [1-(7/3)]

Q. The co-efficient of x7 in the expansion of (1−x4) (1+x)9 is

27

-24

48

-48

(1−x4)(1+9c1​x+9c2​x2+9c3​x3+9c4​x4+9c5​x5 +9c6​x6+9c7​x7+9c8​x8+9c9​x9) Co-eff. of x7=9c7​−7c3​=7c2​−9c3​ =1×29×8​−1×2×39×8×7​ =36[1−37​]

Q. The co-efficient of $x^{7}$ in the expansion of $(1 - x^{4})$ $(1 + x)^{9}$ is