Question

The coefficient of $x^7$ in the expansion of $(1-x^4)(1+x{)}^9$ is

• A. 48
• B. -24
• C. 64
• D. -48

Answer 1

Answer: (D)

-48

$(1-x^4)(1+x{)}^9$

By using expansion of $(1+x{)}^n$ we get,

$(1-x^4)[{}^9{C}_0+{}^9{C}_{1}x+{}^9{C}_2{x}^2+{}^9{C}_3{x}^3+{}^9{C}_4{x}^4+{}^9{C}_5{x}^5+{}^9{C}_6{x}^6+{}^9{C}_7{x}^7+{}^9{C}_8{x}^8+{}^9{C}_9{x}^9]$

Now coefficient of $x^7$ in this expansion will be

$\Rightarrow$ $1\times {(}^9{C}_7)-1{(}^9{C}_3)$

$\Rightarrow$ $\frac{9!}{7!2!}-\frac{9!}{3!6!}$

$\Rightarrow$ $36-84$

$\Rightarrow$ $-48$