Combining Like Terms

To simplify an equation, one of the simplest methods to follow is by combining like terms. But what does like term means? Put simply, you add the coefficients of the terms to solve it quickly.

Take for example, 7x, 2x and 3x, these are all like terms because of the fact that they have like terms. Here x is the term that is common to it all. Hence in order to simplify the equation, you add all the like terms and make it simple. Yes, you can combine the three terms and make it a single term.

Combining like terms doesn’t mean only adding like terms, as you can even subtract the like terms. Take for example, both 5 and 9 and add these two terms because they are both numbers. But you cannot combine 3 and y because both are not like terms, in other words both are not numbers; 3 is a number and y is a letter.

To understand combining like terms more easily, let’s look at the equation:

6x + 2x

So, let’s combine the like terms together. Remember when combining the terms, you need to use the symbols and the numbers before the coefficient.

=(6+2)x
=8x

So, the equation 6x=2x is combined into a single term 8x, because both 6x and 2x had x as a common term which made it quite easy for us to combine the like terms and arrive at a result.

Example 1

Let’s take a look at the example below:

8a + 12a – 7b – 4b + 5a

Here we notice the equation has two common terms, including both a and b. So, let’s combine the like terms.

= (8 + 12 + 5) a + (7-4)b
= 25a + 3b

Example 2

Now let’s look at another example that involves a different kind of equation:

6x + 9x + 6x2 – 8x2 – 2x

Now we can see that we have an equation that involves exponents. Yes, you can see the exponent x2 present before 10 and 7. Since the exponents are the same, that makes them like terms too. Now let’s go about solving the equation:

Remember that 5x and 10x2 are not the same, just because they have an x of them and are not like terms.

6x + 9x + 6x2 – 8x2 – 2x

When you combine the coefficients,

= 6x + 9x – 2x + 6x2 – 8x2
= (6+9-2) x + (6+8) x2
= 13x + 14x2

Hope you have understood the concept of combining like terms through the descriptions and the examples provided above.