Students who are new to high school or at an advanced level often face issues solving mathematical problems. The primary reason behind it is that they fail to recognize like and unlike terms. Simply put, terms are variables that are used in algebraic expressions. A deeper understanding of the concept of terms, their types, the primary factors to keep in mind while dealing with terms, and the difference between the different types of terms helps in solving problems quite easily. If you are one of these students and do not have a clear idea about what is a term in math, then this blog can be of great help to you. Here, we have provided complete details on mathematical terms.
Before we share what a term in math is, it is important to know the concept of an algebraic expression and its components.
What Is An Algebraic Expression?
An algebraic expression is a concept for illustrating numbers or fractional constants, alphabets that do not mention their actual values, and algebraic operators like addition, subtraction, division, multiplication, etc. Typically, in algebra, an expression consists of 4 components. It includes:
- Terms: Numbers, variables, or products that represent their value.
- Coefficients: The integer reproduced with the single or multiple terms’ variable of the algebraic equation.
- Variable: Letters or a symbol used to symbolize a value.
- Constant: Number or the value, which cannot be altered in expression.
What Is A Term In Math?
In an algebraic expression, a term can be a variable or a number. Moreover, it is the product of two or more variables, or even a variable and a number. The algebraic expression or equation is composed of single or multiple terms.
Mentioned below is an example of “What is a term in math?”
4x = 0 (single term)
4x-y = 0 (two terms that are 4x and y).
Consider that the terms are summed up to create an equation; for example, 5xy is the product of 5, x, and y. Moreover, consider another term as -2z. It is the product of z and -2.
Now, incorporate both terms 5xy and -2z in the following way:
5xy + (-2z)
5xy-2z
This derived answer is known as an algebraic equation.
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What Are The Primary Factors Of Terms To Keep In Mind?
Once you have a basic idea of “what a term is in math,” it is essential to understand its 4 essential factors. It includes:
- Concept of a factor: The variables, or numbers, that are multiplied to develop a term are called factors. For example, 4xy is the term that has 3 factors, like 4, x, and y.
- Relation of the power of a term to the power of a factor: If the term contains the power, then the factor of terms is considered as 3x^2 3, x, and x, which is 3 factors.
- Factorization of a factor: The factors must never be factorized further. For example, 4ab cannot be factorized as 4 and ab or 4a and b as ab can be factorized as a and b.
- Position of 1 as a separate factor: 1 cannot be considered an individual factor.
What Are The Different Types Of Terms?
Now that you know “what is a term” in math, you might be curious to learn if it can be categorized or not. Well, there are two categories of terms. They are differentiated based on the variables and the powers.
- Like terms
Like terms refer to specific terms whose variables and exponent power are the same. However, they can have different coefficients of variables. Terms in algebra are similar to each other. In an algebraic expression, these like terms can be combined to elucidate the expression and get the answer in a simple manner. For example, in the algebraic expression 8y + 2y, y is the same variable in the expression, but the coefficients are distinct. To elucidate it further, you can add the two like terms, like 8y + 2y = 10y. Hence, all arithmetic functions like addition, subtraction, multiplication, and division can be executed only on algebraic terms.
- Unlike Terms
Unlike terms refer to those terms that have distinct variables and exponents. It means that the exponents in the variables cannot be raised to the same power. For example, in the algebraic expression, 3x + 9y, x and y are two distinct variables. They also have different coefficients.
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Is It Possible To Perform Addition And Subtraction Of Like And Unlike Terms?
Go through the discussion below to find out whether it is possible to add or subtract like and unlike terms.
· Addition and Subtraction of Like Terms
You can easily add and subtract like terms if you have a basic idea of “what is a term” in math. To perform the same, consider the expression 10x2 – 4x2.
Here, you will find that the variables have a similar exponent but the coefficients are distinct.
You can further explain this expression. For that, you must subtract the same variables from each other. This is achievable since the variables and the exponents are identical regardless of the coefficients being different. The coefficients can be considered as usual numbers along with variables and exponent values. They stay the same after subtraction.
As a result, after simplifying the expression, you get 10x2 – 4x2 = 6x2.
The method of simplifying the expression is also called combining like terms. The addition of like terms is easy, for example, you just need to add the expression 5z + 12z + 32z = (5 + 12 + 32)z = 49z.
· Addition and Subtraction of Unlike Terms
You can never perform addition, subtraction, simplification, or a combination of the expressions for unlike terms. If you know “what a term is in math,” then you will be aware of its constituents, like variables and exponents. There is no relation between variables and exponents expressed in an equation in unlike math. For example, consider the expression 8xy + 6y – 9x – 10x2. The expression has different variables, exponents, and coefficients and hence it cannot be simplified.
Difference Between Like and Unlike Terms
Listed below is the difference between like terms and unlike terms.
| Basis of Comparison | Like Terms | Unlike Terms |
| Concepts | Like terms refer to specific terms that have the same variables and exponents. | Unlike Terms refers to specific terms that have different variables and exponents. |
| Simplification | Terms can be simplified by combining them. | Unlike terms cannot be simplified by combining variables, consonants, and algebraic operators, |
| Conducting Addition and Subtraction | Addition and Subtraction of like terms can be performed together. | Addition and Subtraction of unlike terms cannot be made together. |
| Examples | 12x2 + 5x2 is an illustration of like terms. | 7z – 25r is a pattern of unlike terms. |
| Another name by which they are called | Like terms are also called similar terms. | Unlike terms are also called dissimilar terms. |
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Examples of Like and Unlike Mathematical Terms
The following are examples of mathematical problems based on like and unlike terms.
- Example 1:In the algebraic expression, recognize the like terms 10xy + 3x3 + 21xy + 2x – xy – 6 and elucidate them.
Solution: Given expression: 10xy + 3x3 + 21xy + 2x – xy – 6
Like terms: 10xy + 21xy – xy (since the variables are similar even though the coefficient is different).
Therefore, the like terms are simplified in the following way: 10xy + 21xy – xy = 30xy.
- Example 2:In the algebraic expression, point out the unlike terms: 32x2 – 7y + 4x2 + 43x2 – 5xy – 12x.
Solution: The given expression is 32x2 – 7y + 4x2 + 43x2 – 5xy – 12x
Unlike terms: Here, 7y – 5xy – 12x are unlike terms (since the variable and coefficients are distinct from each other.)
- Example 3:What is the concluding expression in this algebraic expression after merging like terms 4xy + 15x2 + 50xy + 11x2 – 70y3 – 25y?
Solution: From the given expression, first discover the like terms and the unlike terms.
Like terms: The like terms are 4xy + 50xy + 15x2 + 11x2
Unlike terms: The unlike terms are 70y3 – 25y
The final expression can be found after merging the like terms. Thus, 4xy + 50xy + 15x2 + 11x2 = 54xy + 26×2.
Therefore, the final merged expression is 54xy + 26x2 + 70y3 – 25y.
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Conclusion
It is quite pertinent to recognize what is a term in math. Without it, you can never solve any mathematical expression, especially in the case of algebra. The discussion above shares the concept of a mathematical term, its types, and methods of simplifying an expression. Once you learn these concepts, you can easily combine the two types of terms. However, if you still have any confusion or need help solving the problems, connect with our assignment expert immediately. They will solve the issues with the simplest steps and mail you the solution within the mentioned deadline to help you score the desired grades in your math paper.
