### Combining Like Terms

#### Lesson Objective

This lesson is about identifying and combining like terms in algebraic expressions.

#### About This Lesson

When you are given an algebraic expression, usually you will need to simplify the expression.

To do so, first you must learn to identify all the terms in the expression that can be combined. These terms are called 'like terms'.

This lesson shows you the process involved in identifying and combining like terms.

### Study Tips

#### Tip #1

Know how to identify all the terms in the algebraic expression.

#### Tip #2

'Like terms' are terms that have exactly same variables. Also, the exponent (i.e. power) of the variables must be the same.

Now, watch the following math videos to know more.

### Math Video

#### Video on Combining Like Terms

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#### Math Video Transcript

Combining Like Terms

00:00:02.230

The parts of an algebraic expression are called terms. For example, the expression 2 +x +3y has 3 terms. One. Two Three.

00:00:18.000

You can combine terms that have exactly the same variables. This lesson shows you how.

00:00:28.060

Let's say you're asked to simplify x + x + x. To do so, you must able to recognize which of these are like terms.

00:00:38.080

Let's imagine that the variable 'x' is an 'apple'

00:00:42.180

Hence, 'plus x' becomes 'plus apple'. You see that these apples are the same in type and size. So these apples are considered as alike.

00:00:53.190

Since these apples are alike, you can add them up to get 3 apples

00:00:58.180

Now, let's change the apple back to x.

00:01:02.190

You can see now that x+x+x gives 3x. Therefore, all the terms in this expression are like terms.

00:01:12.130

Let's take another example on combining like terms, -x -x -x.

00:01:17.220

Again, imagine that the variable 'x' is an 'apple'. Hence, minus x becomes minus apple.

00:01:26.030

Since these apples are alike, you can add them up to get negative 3 apples

00:01:34.070

Now, let's change the apple back to x.

00:01:38.220

You can see now that -x -x -x gives -3x

00:01:45.180

Let's take another example on combining like terms, x + x + y + y

00:01:51.230

We have a new variable y here. So, let's imagine the variable 'y' is an 'orange'.

00:01:58.220

The each terms in this expression now becomes plus orange, plus apple, plus apple.

00:02:06.000

Now you see that 1 apple plus 1 apple gives two apples. and 1 orange plus 1 orange gives two oranges

00:02:25.050

Let's change these 'apples' back to 'x', you now have x + x which gives 2x.

00:02:25.050

Let's change these 'oranges' back to 'y', you now have y + y which gives 2y.

00:02:36.070

Now, x +x +y +y gives 2x +2y

00:02:42.040

So in summary, you can only add or minus terms that are alike.

00:02:51.050

From the previous examples, you can see that only like terms can be combined

00:02:56.190

Now, let's take a look at more examples on like terms.

00:03:01.090

Both x, and x square, are not like terms. Why?

00:03:06.220

Imagine that, x is an apple. Then x square must be a bigger apple.

00:03:13.160

Even though, both fruits are apples, the difference in sizes make them not alike.

00:03:19.210

Now, let's take a look at x square, and, x square y power of three.

00:03:26.080

These are not like terms. To understand this, let's take x square to be a big apple.

00:03:33.050

Then, x square and y power of three will be like some kind if fruit mixture.

00:03:39.040

Now, it is obvious that these fruits are not alike.

00:03:43.240

How about, x square y power of three, and two x square y power of three?

00:03:49.230

These terms are like terms.

00:03:53.010

To understand this, let x square y power of three, to be a fruit mixture.

00:03:58.230

Then, two x square y power of three, will be 2 times of the same fruit mixture.

00:04:05.150

Now, you see that, the fruits and sizes are the same, and only the number of fruits are different.

00:04:13.010

So, these fruits are alike.

00:04:15.210

That's all for this lesson on combining like terms. Try out the practice questions to strengthen your understanding.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on combining like terms or pick your choice of question below.

- Question 1 on identifying the number of terms in an expression
- Question 2 on identifying like terms in an expression

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