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

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

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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.

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

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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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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These terms are like terms.

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

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

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

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So, these fruits are alike.

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