# How do you combine like terms and order the polynomial by degree with the given problem?

## $\frac{5}{3} {a}^{4} + \frac{2}{5} a - \frac{1}{2} {a}^{4} - \frac{5}{3} a$

Jul 19, 2016

The simplified polynomial will look like $\frac{7}{6} {a}^{4} - \frac{19}{15} a$

#### Explanation:

First off, it would probably be easier to order the polynomial temporarily so we can look at how we need to simplify the terms. We do this simply by looking at the power of the variables. In the given problem we see that we have two terms with $a$ to the fourth power and two terms with $a$ to the first power (no exponent). In order to order the polynomial by degree, we want to have the term with the most power first, until you get to the term with the least power. In other words: biggest to smallest. So let's do that.

$\frac{5}{3} {a}^{4} - \frac{1}{2} {a}^{4} + \frac{2}{5} a - \frac{5}{3} a$

One thing to note: make sure you carry the sign with you, your answer will be wrong if you forget to carry a negative or positive with you term. Note how $- \frac{1}{2} {a}^{4}$ has a negative sign before and after ordering.

Now we should combine our like terms. This can be accomplished by adding the coefficients (the number in front of ${a}^{x}$) of terms with the same power. So we will add $\frac{5}{3} {a}^{4}$ and $- \frac{1}{2} {a}^{4}$, and $\frac{2}{5} a$ and $- \frac{5}{3} a$.

$\frac{5}{3} - \frac{1}{2} = \frac{10}{6} - \frac{3}{6} = \frac{7}{6}$ so our first term will be $\frac{7}{6} {a}^{4}$

$\frac{2}{5} - \frac{5}{3} = \frac{6}{15} - \frac{25}{15} = - \frac{19}{15}$ so our second term will be $- \frac{19}{15} a$

Put it all together and we get our answer: $\frac{7}{6} {a}^{4} - \frac{19}{15} a$