## Introduction to Algebraic Expressions

In mathematics, algebraic expressions mean an expression that consists of variables and constants, along with arithmetic operations such as addition, subtraction, multiplication, and division. For example, 2x +20y = 30 is an algebraic expression as it consists of three terms, i.e. 2x, 20y, and 30. The first two terms, i.e. 2x and 20y, are x and y variables, whereas 30 is a constant. Therefore, algebraic terms are individual elements in an expression that are separated by the plus or minus signs. There are two types of algebraic terms: Like and unlike algebraic terms. This article will learn about the unlike terms and their examples.

## Define Like Term

Like terms are those terms whose variables and exponent power are the same. The coefficients of these variables can be different. Algebraic-like terms are terms that are similar to each other. These like terms in the algebraic expression can be combined to simplify the expression to derive the answer simply.

## Like Terms Examples

For example, This is a like algebraic expression 8y + 2y where y is the same variable in the expression, and the coefficients are different. To simplify it further, we can add the two like terms, i.e. 8y + 2y = 10y. Hence, all arithmetic operations such as addition, subtraction, multiplication, and division can be performed only on like algebraic terms.

## Define Unlike Terms

Unlike terms are those terms whose variables and exponents are different from each other. In an expression, the coefficient is different; the variables are different, i.e. 2 variables and the exponent powers are different; that expression is known to obtain, unlike terms. For example, the algebraic expression 3x + 9y, where x and y are two different variables with different coefficients, is known as unlike algebraic terms.

## Unlike Terms Examples

Unlike terms, the simplification of expressions or combining like terms cannot be done, as the variables and exponents are not similar. For example, $8 x y+6 y-9 x-10 x^2$, as seen here, there are different variables, exponents, and coefficients. This expression cannot be simplified as all the terms are different from each other.

## Solved Examples

Q 1. In the algebraic expression, identify the unlike terms

$-32 x^2-7 y+4 x^2+43 x^2-5 x y-12 x$

Ans: Given expression $32 x^2-7 y+4 x^2+43 x^2-5 x y-12 x$ unlike terms: $7 y-5 x y-12 x$ are unlike terms(as the variable and coefficients are different from each other.)

Q 2. State whether a given pair of terms is of like or unlike terms.

(i) 1,100

(ii) $-29 x,-29 y$

(iii) $14 x y, 42 y x \quad$

(iv) $4 m^2 p, 4 m p^2$

(v) $12 x z, 12 x^2 y^2$

Ans: (i) 1, 100: like terms

(ii) $-29 x,-29 y$ : unlike terms as they have different variables.

(iii) $14 x y, 42 y x$ : like terms

(iv) $4 m^2 p, 4 m p^2$: unlike terms since the power on the variables are different.

(v) $12 x z, 12 x^2 y^2$: unlike terms since the power on the variables are different.

## Practice Problem

Q 1. Is this statement true or false? In the case of like terms, we can add or subtract them together, but unlike terms, we cannot add or subtract.

Ans: True

Q 2. Group the like terms:

$4 x,-3 y,-x, \dfrac{2}{3} x, \dfrac{4}{5} y \text { and } y$

Ans: $4 \mathrm{x},-3 \mathrm{y},-\mathrm{x}, \dfrac{2}{3} \mathrm{x}, \dfrac{4}{5} \mathrm{y}$ and $\mathrm{y}$

Here the like terms are as follows

$4 x,-x, \dfrac{2}{3} x \text { and }-3 y, \dfrac{4}{5} y, y$

## Summary

Like terms are those terms whose variables and exponent power are the same. The coefficients of these variables can be different. Unlike terms are those terms whose variables and exponents are different from each other. Only like terms may be added or removed. While two unlike terms cannot be joined together to form a single term, the sum of one or more like terms does result in a single like the term. In the end, we have seen some solved examples and practice problems. By going through it, we can have much command over the topic.

## FAQs on Unlike terms Definition

1. Can we combine, unlike algebraic Terms?

Unlike algebraic terms, an algebraic expression cannot be combined or simplified further as the expression consists of two different variables.

2. Why do we need to learn about like and unlike terms?

In algebra, one of the most fundamental processes is solving equations. When we solve equations, we are often presented with both like and unlike terms. If we understand how terms work or how to relate them to different situations, then it will be easier for us to solve systems of equations. However, nothing can be too difficult to solve if one properly studies the information and basic methods.

3. What is the significance of algebraic expression?

Algebraic expressions are frequently used by people without being aware of them, but they are still a part of mathematics in some way. Algebraic expressions are used in solving different and complex equations in Mathematics. Algebraic expressions are used for inference tasks in computer programming, for instance. In Economics, algebraic expressions are used to calculate revenue, costs, etc. Algebraic expressions are needed in many areas of Mathematics, including trigonometry, geometry, etc., to solve unknown angles and values. One can improve their aptitude and logical reasoning skills by studying algebra.