Question

The coefficient of $x^7$ in the expansion of $(1- x - x^2 + x^3 )^6$ is

• A. -132
• B. -144
• C. 132
• D. 144

Answer 1

Answer: (B)

-144

Answer 2

$(1 - x - x^2 + x^3)^6 = [(1- x) - x^2 (1 - x)]^6$ $= (1- x)^6 (1 - x^2)^6$ $= (1 - 6x + 15x^2 - 20x^3 + 15x^4 - 6x^5 + x^6)$ $\times (1 - 6x^2 + 15x^4 - 20x^6 + 15x^8 - 6x^{10} + x^{12})$ Coefficient of $x^7 = (- 6) (- 20) + (- 20)(15) + (- 6) (-6) = - 144$