Subtracting unlike terms in algebra is an important concept that helps us to deal with terms that cannot be directly combined due to differing variables or differing powers of variables. In this article, we will learn about, Unlike term definition, subtracting unlike terms and others in detail.
Unlike Terms Definition
Unlike terms are terms in an algebraic expression that do not have the same variables raised to the same powers. In other words, unlike terms cannot be combined or simplified through addition or subtraction because they represent different quantities.
The image added below shows the like and unlike terms.
Examples of Unlike Terms
Consider the algebraic expression: 3x2 + 5x - 7 + 2y
In this expression:
- 3x2 and 5x are unlike terms because they have different exponents on the variable x.
- 3x2 and 2y are unlike terms because they involve different variables (x and y).
- 5x and -7 are unlike terms because one is a variable term and the other is a constant.
Subtraction of Unlike Terms
Subtraction of unlike terms in algebra involves subtracting terms that do not have the same variable or the same power of a variable. Unlike terms cannot be combined through subtraction or addition because they represent different quantities.
Steps to Subtract Unlike Terms
Various steps to subtract, unlike terms.
Step 1: Identify Unlike Terms: Recognize the terms that have different variables or different powers of the same variable.
Step 2: Subtract Each Term Individually: Write the terms with the appropriate subtraction operation between them.
Can we Subtract, Unlike Terms?
- Like terms: Terms that have having same variable or terms having variables with the same exponent power for them are called Like terms. Example: 6x and 16x and 5xy2 and 8xy2
Here, 6x and 16x are called Like Terms because they have the same coefficient of x.
- Unlike terms: Terms that have different variables or terms having variables with different exponent powers for them are called Unlike terms. Example: 7z and 16x and 7x2 and 7x3
Here, 7z and 16x are called Unlike Terms because they have different coefficients of z and x.
Terms with the same variable with different exponents or different variables with the same exponents are called Unlike terms. Only like terms can be subtracted. Unlike terms that cannot be subtracted.
Difference of one or more like terms is a single like term whereas the two unlike terms cannot be subtracted together to get a single term
Let's take a look at this with an example,
If 2x2+3xy+4x+7 is an algebraic expression
Then, 2x2, 3xy, 4x, and 7 are the Terms
- Coefficient of Term: 2 is the coefficient of x2
- Constant Term: 7
- Variables: Here x, y are variables
- Factors of Term: If 2xy is a term, then its factors are 2, x, and y.
Like and Unlike Terms: Example of like and unlike terms,
- Like terms: 4x and 3x
- Unlike terms: 2x and 4y
Read More:
Examples of Subtraction of Unlike Terms
Example 1: Subtract 27z and 16x.
Solution:
Given terms are 27z and 16x
= 27z - 16x
As both terms are unlike terms thus, both terms cannot be subtracted.
Example 2: Identify like terms and unlike terms from the following: 5zy2x, 3y2z, 7xy2z, 3xz2y2, 4x2yz
Solution:
- Like Terms: 5zy2x, 7xy2z
- Unlike Terms: 3y2z, 3xz2y2, 4x2yz
Unlike terms cannot be subtracted
Example 3: Subtract (2x2 - 5xy + 7 + z3) and (3x2 + 4xy - 6 + 2z3)
Solution:
(2x2 - 5xy + 7 + z3) - (3x2 + 4xy - 6 + 2z3)
Add and subtract like terms together,
= (2x2 - 5xy + 7 + z3) - (3x2 + 4xy - 6 + 2z3)
= 2x2 - 5xy + 7 + z3 - 3x2 - 4xy + 6 - 2z3
= 2x2 - 3x2 - 5xy - 4xy + z3 - 2z3 + 7 + 6
= -x2 - 9xy - z3 + 13
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