Simplify the following expression by combining like terms:

Begin by looking for terms to combine. In this case, we only have 2 terms we can combine. Remember, we can only combine terms that have the same exponent and variable.

In this case, the green colors are the only ones which can be combined:

So our answer is:

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms to solve.

and have no like terms and cannot be combined with anything.

5 and -5 can be combined however:

This leaves us with .

First, distribute –5 through the parentheses by multiplying both terms by –5.

Then, combine the like-termed variables (–5x and –3x).

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

Factor the numerator and denominator:

Cancel the factors that appear in both the numerator and the denominator:

To simplify, it can be easier to start by expanding the function:

We can then cancel terms:

and collect them into a more simplified form:

With this problem, you need to distribute the two fractions across each of the trinomials. To do this, you multiply each term inside the parentheses by the fraction outside of it:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms. Since you have a positive and negative , those two terms will cancel out:

Distribute the fraction through both terms in the parentheses.

Simplify the terms.

The answer is:

When simplifying polynomials, only combine the variables with like terms.

can be added to , giving .

can be subtracted from to give .

Combine both of the terms into one expression to find the answer:

and cancel out, leaving in the numerator. 5 and 25 cancel out, leaving 5 in the denominator