### Instruction: Expand $(x+10)(2y+10)$.### Response: We apply the distributive property repeatedly:

\begin{align*}
(x+10)(2y+10) &= x(2y+10) + 10(2y+10)\\
&= x\cdot 2y + x\cdot 10 + 10\cdot 2y + 10\cdot 10\\
&= \boxed{2xy + 10x + 20y + 100}.
\end{align*}. The answer is 2xy+10x+20y+100