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

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

In these expansion ${(1+x)}^9$  be the in the form

${(a+x)}^n={}^n{\text{C}}_0{a}^n+{}^n{\text{C}}_1{a}^{n-1}x+\mathrm{...}+{}^n{\text{C}}_{\text{n}}{x}^n$  then we get  coefficient of $x^7$

$(1-x^4){(1+x)}^9=(1-x^4)\times$ $\left({}^9{C}_0{+}^9{C}_{1}x{+}^9{C}_2{x}^2{+}^9{C}_3{x}^3+\mathrm{...}+{}^9{C}_7{x}^7+\mathrm{...}\right)$

Product of getting $x^7$

Here $1{\times }^9{C}_7{x}^7$  and $-x^4{}^9{C}_3{x}^3$

${\therefore }^9{\text{C}}_7{-}^9{\text{C}}_3$