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

1 Answer

Answer:

#0.8x^2 + 0.995x -0.9=4/5x^2 + 597/600x -9/10#

Explanation:

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

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

So, first things first, #1/5x xx 4x# which is #4/5x^2# as the 4 moves on top and get's divided by 5, and the variable, #x#, gets doubles making #x^2#. Then, #1/5x xx -3/10# which gives us #-3/50x# because the fractions simply multiply across, #1xx3# and #2xx10#. Then all you have left to do is the same with the 3.

You will find that the answer is
#4/5x^2 -3/50x + 12x - 9/10#

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

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

#0.8x^2 + 0.995x -0.9#