Question

The sum of all the coefficients in the binomial expansion of is $(x^2+x-3{)}^{319}$ is?

• A. $1$
• B. $2$
• C. $-1$
• D. $0$

Answer 1

The correct option is C $-1$

Let ${(x^2+x-3)}^{319}={\sum }_{r=0}^{638}{a}_r{x}^r...\left(1\right)$

we need sum of all coefficients $=a_0+a_1+....a_{638}$

subtituting $x=1$ in (1)

${(1+1-3)}^{319}={\sum }_{r=0}^{638}{a}_r$

$\Rightarrow$ $a_0+a_1+....+a_{638}=-1$

$\therefore$ sum of all coefficients $=-1$