Step 1:
First, we distribute the $x$ to each term in the trinomial $x^{2}+2 x y+4 y^{2}$:
\[x \cdot x^{2} = x^{3}\]
\[x \cdot 2xy = 2x^{2}y\]
\[x \cdot 4y^{2} = 4xy^{2}\]
So, $(x-2 y)\left(x^{2}+2 x y+4 y^{2}\right)$ becomes $x^{3} + 2x^{2}y + 4xy^{2} -
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