# How do you multiply (0.2x + 3)(4x -0.3)?

Jul 10, 2018

$0.8 {x}^{2} + 0.995 x - 0.9 = \frac{4}{5} {x}^{2} + \frac{597}{600} x - \frac{9}{10}$

#### Explanation:

First, you should think of things in fractions. $0.2$ is a nasty way to think about the $\frac{1}{5}$ because fractions were made to make things like multiplication easier. So let's rewrite this:
$\left(\frac{1}{5} x + 3\right) \left(4 x - \frac{3}{10}\right)$

From here, you can cross multiply. This means that we will be taking $\frac{1}{5} x$ and multiplying it across to the other parentheses containing $\left(4 x - \frac{3}{10}\right)$. We will do the same with our $+ 3$ in the first parentheses. After that is done, we've finished.

So, first things first, $\frac{1}{5} x \times 4 x$ which is $\frac{4}{5} {x}^{2}$ as the 4 moves on top and get's divided by 5, and the variable, $x$, gets doubles making ${x}^{2}$. Then, $\frac{1}{5} x \times - \frac{3}{10}$ which gives us $- \frac{3}{50} x$ because the fractions simply multiply across, $1 \times 3$ and $2 \times 10$. Then all you have left to do is the same with the 3.

You will find that the answer is
$\frac{4}{5} {x}^{2} - \frac{3}{50} x + 12 x - \frac{9}{10}$

From here, we just want to simply our like terms, meaning the single x's. Then you'll have:
$\frac{4}{5} {x}^{2} + \frac{597}{600} x - \frac{9}{10}$

We can express this in a different way. Since the original question used decimals, we can write the answer as:

$0.8 {x}^{2} + 0.995 x - 0.9$