This lesson shows you how to identify and combine '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.
Know how to identify all the terms in the algebraic expression.
'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.
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Math Video Transcript
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, -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, 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. 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
or pick your choice of question below.
on identifying the number of terms in an expression
on identifying like terms in an expression
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