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# Like Terms|Definition & Meaning

**Definition**

**Like terms** in algebra are those that have the **same variable** to the same power.

Figure 1 illustrates algebraic terms which elaborate the difference between the coefficient, variable, and its power.

The area of **mathematics known as algebra** is used to portray situations or problems using mathematical expressions. Tim’s grandmother, for instance, gave him **several candy bars**. He had five left after **eating a few.** Tim consumed how many candy bars, then? Since we know how many candy bars are still available, the number 5 is referred to as the constant. **Numbers** with a fixed numerical value are known as **constants**.

We’ll use the number x since we don’t know how many candy bars Tim’s grandmother handed him. Variables are represented by the letter x, which stands in for the **unknowable amount**. We can calculate how much he has consumed by **deducting that amount** from the total.

An expression that includes both **variables and constants** as well as an arithmetic operation like **addition, subtraction, multiplication, or division** is referred to as an **algebraic expression** in mathematics.

For instance: Three terms, namely 3x, 19y, and 30 make up the algebraic statement 3x + 19y = 30. The first two terms, 3x and 19y, are variables with 30 being a constant while x and y are both.

Thus**, add or subtract** marks that separate **expression components**, such as algebraic terms, are known as plus signs or minus signs.

The **coefficient **is the number that appears before a phrase. Since it is easier to write “x” and “1x” appears odd, we typically use “x” instead of “1x.” The **symbols (variables)** that we are accustomed to today were not used in algebraic expressions when they were first mentioned. Instead, a **three-step algebraic expression** construction process was used:

“Rhetorical algebra” was the **initial phase**. Equations were now expressed as whole phrases. For instance, “The **object plus two equals three**” is the rhetorical form of a+2=3. The ancient Babylonians set the groundwork for rhetorical algebra, which remained a popular method of algebraic representation until the **16th century**.

Some symbolism emerged in the formulation of algebraic terms in the **second stage**, the Syncopated algebra. These did not, however, include all the traits of **symbolic algebra**.

For instance, using symbolic algebra, there is no restriction on **the number of times** an operation can be applied on one side of an equation. An **algebraic expression** with syncopation is first mentioned in Diophantus’ Arithmetica (third century AD), and then again in Brahmagupta’s Brahma Sphuta Siddhanta (7th century).

The** last stage**, often known as symbolic algebra, is how most of algebra is currently understood and is the point at which **full symbolism emerged**.

Although FranÃ§ois ViÃ¨te provided the foundation for the complete use of symbolism in algebra, some **Islamic mathematicians** like as Ibn al-Banna (13thâ€“14th centuries) and al-Qalasadi (15th century) made **contributions** that can be seen as early steps toward this stage (16th century).

RenÃ© Descartes (17th century) built on the idea that algebra might be used to represent and solve geometry issues at a later time and established the contemporary notation ( known to us as Cartesian geometry).

**Mathematical Operations on Like Terms**

Look at the formula 10×2 – 4×2, where the **variables** have the same exponent but different coefficients. This equation may be made even simpler by removing the identical variables from one another. This is conceivable because, even though **the coefficients differ**, the variables and exponents are the same.

Along with the **variables and exponent values**, the coefficients can be regarded as normal integers because they remain the same after subtraction. As a result, when **the statement is simplified**, we obtain 10×2 – 4×2 = 6×2. Combining **comparable phrases** is the process of making the expression simpler. It is easy to add like words; for instance, add 5z + 12z + 32z to get (5z + 12z + 32z) z.

**Difference Between Like Terms and Unlike Terms**

**Like terms** are the terms having the **same exponents and variables**. Similar concepts can be combined to make them simpler. Similar phrases can be **added and subtracted** together. A pair of phrases that are similar is 13×2 + 5×2.

**Unlike terms** are terms with **different exponents and variables**. Contrary terms cannot be made simpler by joining them. Contrary words cannot be **added or subtracted** together. Similar phrases include **7z and 25r**. Dissimilar words are another name for **unlike terms.**

**Some Example Problems Involving Like Terms**

### Example 1

Write the like terms in the expression x(x + 2) + x(5 + 3x) in simplest form.

### Solution

In order to find the like terms, we have to simplify the expression for that purpose we have to multiply the variable x outside the bracket with inside terms then the expression will become x^{2}+2x+5x+3x^{2} then all terms with variable x are combined 4x^{2}+7x now the expression is 4x^{2} + 7x.

### Example 2

Give the **final expression** after combining the **same terms** of the given expression

4x^{3}+3x^{2}+2x^{2}+5x^{2}+6x+3

### Solution

According to the expression 4x^{3}+3x^{2}+2x^{2}+5x^{2}+6x+3, we have terms with the same variable and three different powers 4x^{3}, 3x^{2}+2x^{2}+5x^{2} and 6x. We add all the like terms 3x^{2}+2x^{2}+5x^{2} which is equal to 10x^{2}. The **final expression** is equal to 4x^{3}+10x^{2}+6x+3.

### Example 3

Write the **like terms** in the expression x(x+2) +x(5x+3)+ 12 in **simplest form**.

### Solution

In order to find the like terms, we have to simplify the expression for that purpose we have to multiply the variable x outside the bracket with inside terms then the expression will become x^{2}+2x+5x^{2}+3x^{2}+12 then **all terms with variable x** are combined 4x^{2}+7x now the expression is 4x^{2}+7x+12.

### Example 4

Give the final expression after combining the same terms of the given expression

5x^{3}+3x^{3}+2x^{2}+5x^{2}+6x+9

### Solution

According to the **expression **4x^{3}+3x^{3}+2x^{2}+5x^{2}+6x+9, we have terms with the same variable and three different powers 4x^{3}+3x^{3}, 2x^{2}+5x^{2} and 6x. We add all the like terms 3x^{3}+4x^{3} which is equal to 7x^{3}. The **final expression** is equal to 7x^{3}+7x^{2}+6x+9.

### Example 5

Illustrate the **coefficients, variable, and power** of the given **expression **

3x^{3}+5x^{3}+4x^{2}+2x^{2}+3x+3

### Solution

First, we have to simplify the expression 3x^{3}+5x^{3}+4x^{2}+2x^{2}+3x+3 we have to add the like terms of x^{3} i.e., 3x^{3}+5x^{3} which is equal to 8x^{3} and x^{2} i.e., 4x^{2}+2x^{2} which is equal to 6x^{2} so the final expression will be equal to 8x^{3}+6x^{2}+3x+3. Figure 2 illustrates the coefficients, variables, and power of the given expression.

### Example 6

Illustrate the like terms with different **variables x and y in given expression**

5x^{3}+3x^{2}+4+8y^{3}+9y^{2}

### Solution

Figure 3 illustrates the like terms with variable x with coefficients 5 and 3 and like terms with variable y with coefficients 8 and 9.

*All images were created using GeoGebra.*