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For the purposes of this definition, an algebraic expression is an expression made up of both variables and constants, in addition to arithmetic operations such as addition, subtraction, multiplication, and division. As an illustration: 3x + 19y = 30 is an algebraic expression since it consists of three terms, namely, 3x, 19y, and 30 and is composed of three variables. The first two terms, 3x and 19y, are variables, but 30 is a constant. The third term, 3x, is also a variable. So algebraic terms are distinct pieces of an equation that can be distinguished by the use of plus or minus marks to separate them. There are two types of algebraic terms: algebraic words that are similar to one another and algebraic terms that are different from one another. Let’s have a look at the definitions of like and unlike algebraic words, as well as some examples.
Like Terms
Like terms are ones in which the variables and the exponent power of the terms are the same as one another. The coefficients of these variables may differ from one another. Algebraic-like concepts are terms that are conceptually related to one another. These similar terms in the algebraic expression can be joined to simplify the statement, allowing for a straightforward derivation of the result. Consider the following example: 8y + 2y is an algebraic expression where y is the same variable in both expressions, but each expression has its own set of coefficients. If we want to make it even more simple, we can combine the two like terms, resulting in 8y + 2y = 10y. As a result, all arithmetic operations, such as addition, subtraction, multiplication, and division, may only be performed on algebraic expressions that are similar to one another.
Addition and subtraction of Like Terms
Consider the following expression: 10×2 – 4×2, where we can see that the variables all have the same exponent, but the coefficients are different from one another. We may make this equation even more straightforward by subtracting the identical variables from one another. This is conceivable because the variables and exponents are the same, regardless of the fact that the coefficients are different. The coefficients, along with the variables and exponent values, can be considered to be normal numbers because their values do not change following subtraction. Following the reduction of the statement to its simplest form, 10x^2 – 4x^2 = 6x^2 is obtained. Combining like terms is the term used to describe the process of simplifying an expression. The combination of comparable terms is straightforward; for example, the formula 5z + 12z + 32z = (5 + 12 + 32)z = 49z can be easily combined.
Unlike Terms
In contrast to terms, terms with variables and exponents that differ from one another are referred to as contradistinguished terms. It is known that an expression will be obtained in an expression where the coefficient is different, the variables are different (i.e. 2 variables), and the power of the exponents is different. This is not the case with terms. In contrast to algebraic terms, the algebraic formula 3x + 9y, where x and y are two separate variables with different coefficients, is referred to as
The addition and subtraction of Unlike Terms
Because the variables and exponents are not the same, the simplification of expressions or the combination of like terms cannot be accomplished on unlike terms. There are several variables, exponents, and coefficients in the equation 8xy + 6y – 9x – 10×2, as can be seen in this example. Because all of the terms are distinct from one another, there is no way to simplify this expression.
Simplification of like and unlike terms in algebraic expression
Like terms can be combined to form a more concise phrase, while Unlike terms cannot be combined to form a more concise phrase.
Difference between like and unlike terms
The following is a list of the distinctions between the two terms, similar terms and unlike terms. Let’s have a look at this.
Like Terms | Unlike Terms |
Terms that use the same exponents and variables as each other. | Terms that use the different exponents and variables as each other. |
There are ways to make things easier by grouping together words that are the same. | There is no way to make things easier by putting together words that are not the same. |
In this case, adding and subtracting terms of the same kind can be done at the same time. | Addition and Subtraction of two different things can’t be done at the same time. |
153z2 + 25z2 is an example of like terms. | 71z – 225x is an example of unlike terms. |
Like terms are known as similar terms. | Dissimilar terms is another name of Unlike terms |
Conclusion
In this post, we spoke about the phrases that are similar and those that are dissimilar. The terms in an algebraic expression were first grasped, and then we discovered that terms could be separated into like and unlike terms. We next learned more about like and unlike terms in more depth. In addition to this, we learned how to conduct addition and subtraction on concepts that are similar and unlike.
