How to simplify unlike terms?

Algebraic Expression is an expression composed of variables and constants as well as algebraic operations like addition, subtraction, and so on. These expressions are composed of terms. Algebraic expressions are equations that are formed when operations such as addition, subtraction, multiplication, division, and so on are performed on any variable.

An algebraic expression (or variable expression) is a combination of terms using operations like addition, subtraction, multiplication, division, and so on.

Example: 5x + 4y – 10, 5x – 15, etc.

Like terms are ones with the same variables and exponent power. These variables’ coefficients might differ. Algebraic-like terms are terms that are similar to one another.

Unlike Terms

The terms where variables and their exponents are different from each other are termed, Unlike terms. In an expression, the coefficient and the variables are different i.e. 2 variables, and their exponent powers are different than the expression obtained is known as, unlike terms.

For example:

The algebraic expression 4m + 8n where m and n are two different variables with different coefficients is known as unlike algebraic terms.

Unlike terms cannot be added or subtracted together but in multiplication and division cases are different.

How to simplify unlike terms?

Solution:

As we know Unlike terms are the terms where variables and their exponents are different from each other, the coefficient of these terms may be the same or different. 

In case of Addition and subtraction

Unlike terms that cannot be simplified to make a single term, only like terms can be added or subtracted.

For Example: 

Add 6x and 6y?

Solution: 

Given : 6x + 6y 

Hence both the given terms are unlike terms, therefore its not possible to add the unlike terms .

Subtract 6x from 8y?

Solution:

Given: 8y – 6x 

  Hence both the terms are unlike terms, therefore its not possible to subtract unlike terms .

In case of Multiplication and Division 

Unlike terms can be multiplied or divided to make a single term.

For Example: 

Multiply 6x and 6y?

Solution:

Given terms are unlike terms 

now multiply 

                 = 6x × 6y

                 = 36xy 

Divide 12x² and 6x?

Solution: 

Given terms are unlike terms 

Now divide : 12x² / 6x 

After simplifying we will get 

           = 2x

Hence unlike terms can be simplified only in case of multiplication and division .but in case of Addition and subtraction unlike terms cannot be simplified ..

Practice Problem on the simplification of Unlike Terms

Problem 1: Identity-like terms and unlike terms from the following given terms

5zy²x, 4y²z, 3xy²z, 6xz²y², 9x²yz

Solution:

Like Terms : 5zy²x ,3xy²z

Now Unlike terms = 4y2z , 6xz²y², 9x²yz 

Problem 2: Add 3z & 15x.

Solution:

Here the given terms are 3z & 15x, both are unlike terms

3z + 15x is a term but this cannot be added because both have different variables with different coefficients and are unlike terms

Problem 3: Subtract 6z & 3x.

Solution:

Here the given terms are 6z & 3x,

= 6z – 3x is a unlike term but this cannot be subtracted because both have different variables with different coefficients and are unlike terms.

Problem 4: Multiply 3a, 2a, 5b?

Solution:

Given terms are 3a , 2a and 5b

here 3a and 2a are like terms

=  (3a × 2a) × 5b

= 6a² × 5b

now multiply unlike terms

= 30a²b

Problem 5: Divide 15x³ and 3x²?

Solution:

Given terms are 15x³ and 3x² 

both are unlike terms as they have different coefficients and different exponents 

now divide:

                       = 15x³ / 3x²

                       =  15/3 × x³/x²

                       = 5x