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

The correct option is B -144

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