# 1964 AHSME Problems/Problem 20

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## Problem 20

The sum of the numerical coefficients of all the terms in the expansion of $(x-2y)^{18}$ is:

$\textbf{(A)}\ 0\qquad \textbf{(B)}\ 1\qquad \textbf{(C)}\ 19\qquad \textbf{(D)}\ -1\qquad \textbf{(E)}\ -19$

## Solution

For any polynomial, even a polynomial with more than one variable, the sum of all the coefficients (including the constant, which is the coefficient of $x^0y^0$) is found by setting all variables equal to $1$. Note that we don't have to worry about whether a constant is a coefficient of an "invisible $x^0y^0" term, because there is no such term here. Setting$ (Error compiling LaTeX. ! Missing $inserted.)x=y=1$gives$(-1)^{18}$, which is equal to$1$, which is answer$\boxed{\textbf{(B)}}$.

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