Question

Find the coefficient of $x^{10}$ in the expansion of $\frac{{(1+x)}^2}{{(1-x)}^3}$

• A. 40
• B. 50
• C. 60
• D. None of the above

Answer 1

Answer: (A)

40

${(1+x)}^2$.${(1-x)}^{-3}$

$(1+2x+x^2)$$(...............{+}^{3+8-1}{C}_8.x^8{+}^{3+9-1}{C}_9.x^9{+}^{3+10-1}{C}_{10}.x^{10}..........)$

So, to get coefficent of$x^{10}$

(..........................+(${}^{10}{C}_8$+2${}^{11}{C}_9$+${}^{12}{C}_{10}$).$x^{10}$+.........................)

Hence the coefficent is ${}^{10}{C}_8$+2${}^{11}{C}_9$+${}^{12}{C}_{10}$=(40+110+60)=220