Question

Find the coefficient of $x^7$ in ${(1-x+x^2+x^3)}^6$

• A. $144$
• B. $-144$
• C. $-120$
• D. $120$

Answer 1

Answer: (B)

$-144$

$(1-x-x^2+x^3{)}^6=(1-x{)}^6(1-x^2{)}^6=({{}^{6}C}_0-{{}^{6}C}_{1}x-+.....+{{}^{6}C}_6{x}^6\left)\right({{}^{6}C}_0-{{}^{6}C}_1{x}^2-+.....+{{}^{6}C}_6{x}^{12})$

Now sufficient of $x^7$ is ${{}^{6}C}_1{{}^{6}C}_3-{{}^{6}C}_3{{}^{6}C}_2+{{}^{6}C}_5{{}^{6}C}_1$