Question

The coefficient of x¹³ in the expansion of (1 – x)⁵ (1 + x + x² + x³)⁴ is

a. 4

b. –4

c. 0

d. none of these

Answer 1

Correct option is a. 4

Coefficient of x¹³ in = (1 – x)⁵ (1 + x + x² + x³)⁴ = (1 – x)⁵ ((1 + x)(1 + x²))⁴

= (1 – x) {(1 – x)(1 + x)(1 + x²)}⁴

= (1 – x) {(1 – x⁴)⁴

= (1 – x) (1 – 4x⁴ + 6x⁸ – 4x¹² + x¹⁶)

\(\therefore\) coefficient of x¹³ is –1 × –4 = 4