Expand the following product: $\frac{2}{5}\left(\frac{5}{x} + 10x^2\right)$.
Let's just directly apply the distributive property here. The distributive property is $a\left(b+c\right)=ab+ac$. In this case, $a$ is $\frac{2}{5}$, $b$ is $\frac{5}{x}$ and $c$ is $10x^2$. So applying the distributive property, we get $\frac{2}{5}*\frac{5}{x} + \frac{2}{5}*10x^2$. When we multiply $\frac{2}{5}*\frac{5}{x}$, we get $\frac{2*5}{5*x}$. And when we multiply $\frac{2}{5}*10x^2$, we get $\frac{20x^2}{5}$. $\frac{2*5}{5*x}$ simplifies to $\frac{2}{x}$. $\frac{20x^2}{5}$ simplifies to $4x^2$. So the expanded form of the product is $\frac{2}{x} + 4x^2$. And that's our answer.

