Example 1

3x² + 47y³–7x² + 4ay

In this example, there are four terms: 3x², 47y³, –7x², and 4ay

Notice that the negative stays with the term.

Now, in Algebra, we can simplify polynomials by combining like terms. Like terms are terms that have exactly the same variables, and those variables have exactly the same exponential values. In our example, 3x², and –7x² are like terms. Both have an x² as the variable.

Once you identify the like terms, you can combine them by adding or subtracting the constants. Here is what would happen in our example:

-4x² + 47y³ + 4ay, since 3-7 = -4

When combining like terms, the exponents and variable stay the same. We just work with the constants.

Example 2

5x² + 7y⁴– 8y⁴ + 10x²

Start by identifying the like terms:

5x², 10x²
7y⁴–8y⁴

Add these values. You get 15x²–1y⁴

Example 3

7ab + 9ac – 10abc + 15ac + 4ab – 20b + 5a

Start by identifying the like terms:

7ab, 4ab
9ac, 15ac

Even though this is a long expression, these are the only pairs of like terms. Notice that they have the exact same patterns of variables. The expression simplifies like this:

11ab + 24ac –10abc –20b + 5a

Example 4

6x²y + 8xy²– 10x²y – 15xy + 9xy²

Identify like terms:

6x²y, -10x²y
8xy², 9xy²

Simplify

-4x²y + 17xy²–15xy