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

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Solution

Let
$(x^{2} + x - 3)^{319} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{638} x^{638}$
Putting $x = 1$ in above equation, we get
$(1 + 1 - 3)^{319} = a_{0} + a_{1} + a_{2} + \dots + a_{638} \Rightarrow a_{0} + a_{1} + a_{2} + \dots + a_{638} = - 1$
Hence, required absolute value will be $1.$

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