Answer
$13440x^{4}y^{6}$
Work Step by Step
We find the term with $x^4$ in the expansion of $(x+2y)^{10}$ by using Binomial Theorem coefficients:
$\left(\begin{array}{l}
10\\4\end{array}\right)(x)^{4}(2y)^{6}=210*x^4*64y^6=13440x^{4}y^{6}$
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