Addition of Like Terms

Addition of Like Terms – Definition, Rules, Examples | How to Add Like Terms to Simplify Polynomials?

An algebraic expression is a mathematical expression composed of Constants and Variables, as well as operations like addition and subtraction. A variable in an expression is a term with an uncertain value, whereas a constant term has a known value. A coefficient is a numerical number that goes with a variable.  We can only do addition and subtraction on like terms. Let’s learn the definition, rules, methods for the addition of like terms, and related solved examples in this article.

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What is meant by the Addition of Like terms?

Generally, terms in an algebraic equation are separated by addition or subtraction. Let’s have a look at an algebraic equation before we learn about the addition of like terms. Like terms have almost the same variables and exponents as unlike terms, whereas unlike terms include different variables.

Methods on How to Add Like Terms

When adding algebraic expressions, you must first gather the like terms and then add them. The like term whose coefficient is the sum of the coefficients of the like terms is the sum of the coefficients of the like terms.

There are two approaches to addressing the algebra addition problem.

Horizontal Approach: In this procedure, all phrases must be written in a horizontal line and then arranged to gather all groupings of like terms. These related keywords are then included.

Column Method: In this manner, each statement must be written in a distinct row, with like words grouped one below the other in the column. The terms must then be added column by column. Let’s have a look at some examples and rules.

Rules for Addition of Like Terms

There are certain rules we need to follow while adding like terms and they are as follows

Rule 1: When all terms in an expression are positive, combine their coefficients and variables, and the power of like terms remains constant. In expressions, provide instances of like terms:

Example: Combine the phrases 2pq, 5pq, and 4pq.

3pq, 8pq, and 5pq are synonymous words in this context.

3pq + 8pq + 5pq =

3 + 8 + 5 = 16 is the sum of the coefficients.

As a result, 3pq + 8pq + 5pq = 16pq.

Rule 2: When all terms in an equation are negative, add their coefficients without considering their negative sign, and then prefix the result with the minus sign.

Take note: Be mindful of the signs. If an expression contains a negative sign before it, take it into account when adding/subtracting.


Solve -9xy, -4xy, and -5xy in Example 1.

The terms given are -9xy, -4xy, and -5xy.

9 + 4 + 5 = 18 are the coefficients of the given terms.

As a result, the sum of -9xy, -4xy, and -5xy is (-9xy) + (-4xy) + (-5xy) = -18xy.

As a result, the outcome is -18xy.

Rule 3: If all terms do not have the same sign, apply the same rule as for integer addition.

Example: Add 9x by -4x.

= 9x + (-4x)

= 9x – 4x

= 5x

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Combining Like Terms Examples

1. Simplify the expression xy+ 8xy and 9xy

9xy, 8xy, and xy are like terms here.

When all of the terms are positive, sum their coefficients while keeping the variables and power of the similar terms constant.

The total of the coefficients = 9 + 8 + 1 [xy = 1xy]

As a result, 9xy + 8xy + xy = 17xy.

2. Simplify 6x³ + 4x³ + 8y² + 2y²

In this case, 6x³ + 4x³ are like terms.

In addition, 8y² +2y² are like terms.

To combine two or more like terms, add their numerical coefficients and produce another like term with the sum as the numerical coefficient of the resultant term.

6x³ + 4x³ = 10x³

8y² +2y² = 10y²

As a result, the solution is 10x³ + 10y².

3. Add the like terms -4ab, -5ab, and -ab

Without taking into account the negative signs, the coefficients of the given terms are 4, 5, and 1; and 4 + 5 + 1 = 10.

When all of the terms are negative, add their coefficients without taking into account their negative signs, and then prefix the result with the minus sign (-).

As a result, the sum of -4ab, -5ab, and –ab = -10ab.

Specifically, (-3ab) + (-5ab) + (-ab) = -9ab

FAQs on Adding Like Terms

1. Is it true that algebraic expressions are polynomials?

Polynomials do not exist in all algebraic expressions. Polynomials, on the other hand, are also algebraic expressions. The distinction is that polynomials only contain variables and coefficients with mathematical operations (+, -, ), whereas algebraic expressions include irrational values in the powers as well

Also, polynomials are continuous functions (for example, x2 + 2x + 1), whereas algebraic expressions are not always continuous (for example, 1/x2 – 1 is not continuous at 1).

2. Can you add more similar terms?

Similar terms can be added or subtracted. The variable section remains unchanged; we simply add the coefficients (the numerical portion of the terms). Unlike terms cannot be subtracted or added from each other.

3. Are pq and qp like terms?

Without a doubt. The variables in the words pq and qp are the same. These terms are denoted by p*q and q*p, respectively. This is comparable to 5*3 and 3*5; regardless of the sequence of multiplication, they produce the same number in mathematics. As a result, pq and qp are said to be similar concepts.

4. How do you distinguish between concepts that are like and those that are unlike?

Examine the variable component of the words, and it will be simple to distinguish between like and unlike terms. As like terms have the same variable component, unlike terms have a separate variable portion.

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