What are Like Terms & How to Combine Them

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

4x2 + 3x2 +2x2 = 11x2

 

3xy2 + 5xy2 = 7xy2

 

3x2y2 – x2y2 = 2x2y2

Cautions

Terms like x2yz, xyz2 and xy2z look a lot alike, but they cannot be combined. Write the terms carefully while solving the problems.

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:

4x2y + 3xy2 + 5x2y + xy2

Now again adding the like terms. In this example,

4x2y and 5x2y are like terms.

3xy2 and xy2 are like terms.

we get,

4x2y + 5x2y + 3xy2 + xy2 = 9x2y + 4xy2

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:

5x2y, 4xz, 3x5, y2z.

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:

5xz2 * 4yz = 20xyz3

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:

4y3 * 7y2z = 28y5z

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:

20xyz3/4yz = 5xz2

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:

45x3y3z3/ 5xy2z = 9x2yz2

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.