Question 548846
I have no idea what you're doing. Let's start from the beginning. First, you should make your notation clear by correctly placing parentheses, and don't place operations such as * or + unless you clearly know what number/expression you want to use. Knowing LaTeX or the notation on algebra.com can help (here I use LaTeX since it is more widely used, and is neater).


You want to do the operation


*[tex \LARGE (\frac{1}{10}x^2 - \frac{1}{2}x(-\frac{3}{10})) + (\frac{1}{2}x^2 + \frac{1}{4}x(-\frac{1}{5}))].


First, do the innermost operations (in this case, multiplying variable expressions by constants) to get


*[tex \LARGE (\frac{1}{10}x^2 + \frac{3}{20}x) + (\frac{1}{2}x^2 - \frac{1}{20}x)]


Then add. You cannot combine x^2 and x terms together, similar to the fact that you cannot combine apples and oranges and obtain apples. Adding, we get


*[tex \LARGE (\frac{1}{10} + \frac{1}{2})x^2 + (\frac{3}{20} - \frac{1}{20})x]


*[tex \LARGE = \frac{3}{5}x^2 + \frac{1}{10}x]

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For the multiplication one, we multiply the -2/3 with the 1/3, so our expression is equivalent to


*[tex \LARGE (-\frac{2}{9}x^2)(\frac{1}{2}x - \frac{1}{2})]


Then multiply. Be careful about the negative signs.


*[tex \LARGE = (-\frac{2}{9}x^2)(\frac{1}{2}x) + (-\frac{2}{9}x^2)(-\frac{1}{2})]


*[tex \LARGE = -\frac{1}{9}x^3 + \frac{1}{9}x^2]