Find the sum of all coefficients in expansion of $(x^2+2x)^{20}$.

Question

Find the sum of all coefficients in expansion of $(x^2+2x)^{20}$.

Is there a specific method or formula for this?

Answer 1

The sum of the coefficients of a polynomial is just the value that such polynomial takes in $1$, hence: $$\sum_{n\geq 0}[x^n](x^2+2x)^{20} = (1+2)^{20} = 3^{20}.$$