Question

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

• A. 27
• B. -24
• C. 48
• D. -48

Answer 1

The correct option is D -48

Given expansion is
$(1-x^4)(1+x{)}^9$
$=(1-x^4){(}^9{C}_0{+}^9{C}_{1}x{+}^9{C}_2{x}^2{+}^9{C}_3{x}^3+...{.}^9{C}_9)$
Now, the coefficient of $x^7$ in the above expansion will be sum of two terms ${}^9{C}_7$ and ${-}^9{C}_3$
So, coefficient of $x^7$ is ${}^9{C}_2{-}^9{C}_3=-48$