Like Terms in Algebra – Examples and Practice problems

Like terms are terms of algebraic expressions that have the same variables with the same exponents. These terms can be added to simplify an algebraic expression. Constant terms are also considered like terms.

Here, we will look at 10 examples with answers of like terms in algebraic expressions. Then, we will look at some practice problems.

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Examples of like terms

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Solving problems with like terms in algebra.

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ALGEBRA
Examples of like terms

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Solving problems with like terms in algebra.

See examples

10 Examples with answers of like terms

Each of the following examples has a detailed solution. If you need to do a revision of like terms, you can visit our main article with definitions.

EXAMPLE 1

Determine the terms that are like terms of $latex 6x^2$.

$latex 2x^2~~$ $latex ~~5x~~$ $latex ~~3x^3~~$ $latex ~~4x^2$

The given term is $latex 6x^2$. We note that it has a variable, x, raised to the power of 2. Then, we analyze each of the given terms

  • $latex 2x^2$ has the same variable x, raised to the power of 2. It is a like term.
  • $latex 5x$ has the same variable x, but it is not raised to the power of 2. It is not a like term.
  • $latex 3x^3$ has the same variable x, but it is not raised to the power of 2. It is not a like term.
  • $latex 4x^2$ has the same variable x, raised to the power of 2. It is a like term.

The like terms of $latex 6x^2$ are $latex 2x^2~$ and $latex ~4x^2$.

EXAMPLE 2

Which of the following are like terms of $latex 2xy^2$?

$latex 3xy^2~~$ $latex ~~2xy~~$ $latex ~~5xy^3~~$ $latex ~~4xz^2$

We want terms with $latex xy^2$. Analyzing each of the given terms, we have:

  • $latex 3xy^2$ has the same variables with the same exponents. It is a like term.
  • $latex 2xy$ has the same variables, but with different exponents. It is not a like term.
  • $latex 5xy^3$ has the same variables, but with different exponents. It is not a like term.
  • $latex 4xz^2$ does not have the same variables. It is not a similar term.

The like term of $latex 2xy^2$ is $latex 3xy^2$.

EXAMPLE 3

Identify like terms in $latex -2x^2y$.

$latex 3y^2z~~$ $latex ~~-3xy^2~~$ $latex ~~4x^2y~~$ $latex ~~5x^2z$

We have to find terms with $latex x^2y$. Then, we have:

  • $latex 3y^2z$ does not have the same variables. It is not a like term.
  • $latex -3xy^2$ has the same variables, but with different exponents. It is not a like term.
  • $latex 4x^2y$ has the same variables with the same exponents. It is a like term.
  • $latex 5x^2z$ does not have the same variables. It is not a like term.

The like term of $latex -2x^2y$ is $latex 4x^2y$.

EXAMPLE 4

Which of the following are like terms of $latex 4x^2y^3z$?

$latex 3xy^2z^2~~$ $latex ~~2x^2y^3z~~$ $latex ~~4x^2y^3z^2~~$ $latex ~~-2x^2y^3w$

In this case, we need to find terms with $latex x^2y^3z$. Looking at each given term, we have:

  • $latex 3xy^2z^2$ has the same variables, but with different exponents. It is not a like term.
  • $latex 2x^2y^3z$ has the same variables and the same exponents. It is a like term.
  • $latex 4x^2y^3z^2$ has the same variables, but with different exponents. It is not a like term.
  • $latex -2x^2y^2w$ does not have the same variables. It is not a like term.

The like term of $latex 4x^2y^3z$ is $latex 2x^2y^3z$.

EXAMPLE 5

Combine the like terms of the following expression:

$$2x^2+2x+5x+4x^2+3x+2x^2$$

To combine like terms, we can start by identifying all the like terms:

  • $latex 2x^2~$, $latex ~4x^2~$ and $latex ~2x^2$
  • $latex 2x~$, $latex ~5x~$ and $latex ~3x$

Now, we add these terms and we have:

$$(2x^2+4x^2+2x^2)+(2x+5x+3x)$$

$$=8x^2+10x$$

EXAMPLE 6

Simplify the following expression by combining like terms:

$$3y^2+2y+y^2+5+4y+3+2y^2+4$$

Identifying like terms, we have:

  • $latex 3y^2~$, $latex ~y^2~$ and $latex ~2y^2$
  • $latex 2y~$ and $latex ~4y~$
  • $latex 5~$, $latex ~3~$ and $latex ~4$

Adding the like terms, we have:

$$(3y^2+y^2+2y^2)+(2y+4y)+(5+3+4)$$

$$=6y^2+6y+12$$

EXAMPLE 7

Combine the like terms of the following expression:

$$2x^3+4x-2x^2+4x^2-5x^3+5x-3x^2$$

We have the following like terms:

  • $latex 2x^3~$, and $latex ~-5x^3$
  • $latex -2x^2~$, $latex ~4x^2~$ and $latex ~-3x^2$
  • $latex 4x~$ and $latex ~5x$

Adding these terms, we have:

$$(2x^3-5x^3)+(-2x^2+4x^2-3x^2)+(4x+5x)$$

$$=-3x^3-x^2+9x$$

EXAMPLE 8

Simplify the following expression by combining like terms:

$$2xy^2+4x^2y+3xy^2+5+4x^2y+3+2xy^2+2$$

We have the following like terms:

  • $latex 2xy^2~$, $latex ~3xy^2~$ and $latex ~2xy^2$
  • $latex 4x^2y~$ and $latex ~4x^2y~$
  • $latex 5~$, $latex ~3~$ and $latex ~2$

Adding these terms, we have:

$$(2xy^2+3xy^2+2xy^2)+(4x^2y+4x^2y)+(5+3+2)$$

$$=7xy^2+8x^2y+10$$

EXAMPLE 9

Combine the like terms of the following expression:

$$3ab^2-2a^2b+5ab^2-ab+3a^2b+2ab+2ab^2-a^2b$$

Let’s start by identifying the like terms of the given expression:

  • $latex 3ab^2~$, $latex ~5ab^2~$ and $latex ~2ab^2$
  • $latex -2a^2b~$, $latex ~3a^2b~$ and $latex ~-a^2b~$
  • $latex -ab~$, and $latex ~2ab$

Adding the like terms, we have:

$$(3ab^2+5ab^2+2ab^2)+(-2a^2b+3a^2b-a^2b)+(-ab+2ab)$$

$$=10ab^2+ab$$

EXAMPLE 10

Combine the like terms of the following expression:

$$xyz^2-2x^2yz+5xy^2z+4x^2yz+3xy^2z-2x^2yz+2xyz^2$$

We have the following like terms:

  • $latex xyz^2~$, and $latex ~2xyz^2$
  • $latex -2x^2yz~$, $latex ~4x^2yz~$, $latex -2x^2yz$
  • $latex 5xy^2z~$ and $latex ~3xy^2z$

When we add these terms, we have:

$$(xyz^2+2xyz^2)+(-2x^2yz+4x^2yz-2x^2yz)+(5xy^2z+3xy^2z)$$

$$=3xyz^2+8xy^2z$$


Like terms – Practice problems

Like terms Quiz
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What is the coefficient of $latex x^2y$ when we combine like terms? $$2xy^2+2x^2y+3x^2y-4xy^2-3x^2y-xy^2-4x^2y$$

Write the value in the input box.

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