**What are Like Terms?**

Like terms are terms that consist of the same variables that are raised to the same exponent. Only the constants or coefficients are not the same. In an algebraic expression, we can combine only like terms. We combine the like terms for shortening and simplification of the algebraic expressions, so that we may work with the expressions more easily.

For combining the like terms, we simply add the constants or coefficients and keep the variables as they are. We can not combine unlike terms because that is like trying to add bananas and carrots!

**Examples of Like Terms**

**4x ^{2 }+ 3x^{2} +2x^{2} = 11x^{2}**

**3xy ^{2} + 5xy^{2} = 7xy^{2}**

**3x ^{2}y^{2} – x^{2}y^{2} = 2x^{2}y^{2}**

**Cautions**

Terms like **x ^{2}yz**,

**xyz**and

^{2}**xy**look a lot alike, but they cannot be combined. Write the terms carefully while solving the problems.

^{2}z**Do not get confused**

While solving terms like** xy** or **yx**, do not get confused as they obey the associative and commutative properties. Both the previous terms are alike.

**Solving of Like Terms**

**Like Terms with Linear Expressions of a Single Variable**

Linear expressions are the expressions in which all variables are to the power of 1. So, there are no squared or cubic terms.

**Example:**

2x + 5 + 3x + 2

We have to combine the terms that are the same; all the terms that are only constants need to group together and simplify, do the same with algebraic terms.

As

2x + 3x + 5 + 2 = 5x + 7

**Like Terms with Different Letters**

On some occasions, terms have more than one variable that is multiplying or dividing together.

**Example:**

2xy + 5x + 3xy

In this example,

2xy and 3xy, are like terms that will be adding together to simplify the above expression; hence we solve it as,

2xy + 3xy + 5x = 5xy + 5x

**Like Terms with Powers**

The terms of the same powers or exponents have to be grouped together. Such terms can also include multiple variables and powers.

**Example:**

4x^{2}y + 3xy^{2}+ 5x^{2}y + xy^{2}

Now again adding the like terms. In this example,

4x^{2}y and 5x^{2}y are like terms.

3xy^{2} and xy^{2} are like terms.

we get,

**4x ^{2}y + 5x^{2}y + 3xy^{2} + xy^{2} = 9x^{2}y + 4xy^{2}**

**Unlike Terms**

Unlike terms are two or more than two terms that are not the same, i.e. either they do not have the same variable or power. The order of the variables does not matter unless there is power.

**For example:**

5x^{2}y, 4xz, 3x^{5}, y^{2}z.

All the mentioned terms are unlike terms as their variables and powers or exponents are not the same.

**Solving the Unlike Terms**

we cannot add or subtract unlike terms. we can just multiply or divide the unlike terms.

**Multiplication of Unlike Terms**

In the process of multiplication of unlike terms, we can simply multiply the constants and combine the variables. if they contain any same variable, their powers or exponents are added together.

Example:

5xz^{2}* 4yz = 20xyz^{3}

In this example, we have simply multiplied the constants, i.e. **5*4 = 20**,

for variables, we combine different variables and added the power of the same ones, i.e. the power of z becomes **2+1=3** after multiplication.

**Another example:**

4y^{3}* 7y^{2}z = 28y^{5}z

In this example, we have simply multiplied the constants, i.e. **4*7 = 28**,

for variables, we combine different variables and added the power of the same ones, i.e. the power of y becomes **3+2=5** after multiplication.

**Division of Unlike Terms**

We can divide the unlike terms by dividing the constants and combining the variables.

**Example:**

20xyz^{3}/4yz = 5xz^{2}

In this example, we have simply divided the constants, i.e. **20/4 = 5,**

for variables, we combine different variables and subtracted the power of the same ones, i.e. the power of z becomes **3-1=2** after division.

**Another Example:**

45x^{3}y^{3}z^{3}/ 5xy^{2}z = 9x^{2}yz^{2}

In this example we have simply divided the constants, i.e. **45*5 = 9**,

for variables, we combine different variables and subtracted the power of same ones, i.e.

- the power of x becomes
**3-1=2**after division. - the power of y becomes
**3-2=1**after division. - the power of z becomes
**3-1=2**after division.