The four basic operations in mathematics are subtraction, addition, multiplication, and division. The sum of similar terms is a single term whose coefficient equals the sum of the specified terms’ coefficients. The rules for subtracting similar terms are the same as those for subtracting integers. Let us study the Concept of Adding and Subtracting Like Terms so that we may apply them to both like and unlike terms.
What is meant by Adding and Subtracting of Like Terms?
When adding and subtracting algebraic equations, we first divide the terms into two categories: like and unlike terms. Like terms are combined and simplified. It is important to note; We can just combine terms that are similar by adding or subtracting them. Terms that are diametrically opposed cannot be mixed by adding or subtracting. Terms with the same variables and exponents are known as ‘like terms,’ whereas terms with different variables are known as ‘unlike terms.’
How do you Add and Subtract Like Terms?
As previously stated, addition and subtraction may only be done on similar terms that is like terms. To add and subtract algebraic equations, we must first find all like terms, group them together, and then simplify. We have an algebraic equation that has been added and subtracted.
It is necessary to keep in mind that we can only subtract or add like terms when subtracting or adding algebraic expressions. Subtraction and addition of algebraic equations or expressions can be done in two ways: horizontally or vertically.
Addition of Like Terms
A mathematical expression is made up of constants and variables, coefficients, and operators as mentioned in the above examples. So, while adding and subtracting algebraic expressions is comparable to adding and subtracting numbers, we must arrange like and unlike terms together when dealing with algebraic expressions. When you are adding or subtracting algebraic equations, you need to be aware of the terms like and unlike. To add or subtract algebraic expressions, there are two techniques.
Horizontal Approach
Let us use the horizontal approach to solve these expressions: (p + 5q + 2m + 4) + (3p + 2q + 6m + 2). To do this, we will first combine similar phrases, write them together, then add them to arrive at the solution.
- Step 1: Separate the brackets as follows: p + 5q + 2m + 4 + 3p + 2q + 6m + 2
- Step 2: Add the like terms together to get the simplified expression: 4p + 7q + 8m + 6.
Column Technique
The column technique requires expressions to be written column-by-column, one below the other, with like words in the same column. Then, for each column, we add the numerical coefficient (like terms) and write the total below it, followed by the common variable. Let’s use the column method to add the same expressions.
p + 5q + 2m + 4
+ 3p + 2q + 6m + 2
—————————
4p + 7q + 8m + 6
—————————-
Make the most out of the 6th Grade Math Concepts similar to this concept and get a strong grip on the fundamentals.
Subtraction of Like Terms
To subtract two or more algebraic expressions, the terms in an algebraic expression must be classified into two types: like and unlike terms. Then add up the like terms and deduct them proportionally. The horizontal approach demands writing the expressions to be subtracted below the expression from which they are to be subtracted. Every term has to be removed has its sign inverted, and the resultant expression is added normally.
We must be careful with the signs when subtracting one algebraic statement from another. It should be noticed that if there is a subtraction sign before the brackets, we must reverse all of the signs after the brackets are opened.
Horizontal Approach
Let’s try this Using the horizontal technique: (8a + 4b – 2c) – (5a – 2b + 7c + 9).
- Step 1: Open the brackets as follows: 8a + 4b – 2c – 5a + 2b – 7c -9 (Note how the signs in the second equation have changed.)
- Step 2: Add the similar terms together to create the reduced expression: 3a + 6b – 9c – 9.
Columns Method approach
Let’s use the column approach to subtract the identical terms. As we arrange the two expressions, one on top of the other, we modify all of the signs of the second number, as shown below, and then simplify the expressions based on their signs.
The steps to accomplish subtraction of algebraic expressions via column approach are as follows:
- Step 1: Place one expression underneath the other. Make sure you’ve put similar phrases in the same column. If a phrase, such as 2×2, does not have a corresponding term in the second expression, either write below it or leave that column blank.
- Step 2: Replace the operators in the final row (second expression), for example, (+) with (-) and (-) with (+).
- Step 3: Especially when considering the altered signs, add the numerical coefficient of each column (like terms) and write it below it in the same column, followed by the common variable.
8a + 4b – 2c
(-) 5a – 2b + 7c + 9
(-) (+) (-) (-)
—————————–
3a + 6b – 9c – 9
—————————–
Important Note
- It is usually preferable to remove two expressions at once. Never use the column method to add three or more expressions together.
- If there is a negative sign outside the brackets, the operators inside the brackets must be altered.
- We consider it positive if there is no sign written with the first term of the algebraic equation. 6x, for example, is equivalent to +6x.
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Adding and Subtracting Like Terms Examples
1. Combine the like terms and then simplify 9a – 3b + 7ab + 8b – 5ab – 4a
9a – 4a +8b – 3b + 7ab – 5ab → arrange the like terms
= (9 – 4)a + (-3 + 8)b + (7 – 5)ab → combine like terms
= (5)a + (5)b + (2)ab → simplify
= 5a + 5b + 2ab
2. Combine the like terms and simplify -8z5 + 3 – 6z3 + 5z + 7z3 – 5z5 – z.
= -8z⁵ – 5z⁵ – 6z³ + 7z³ + 5z – z + 3 → arrange the like terms.
= (-8 – 5)z⁵ + (-6 + 7)z³ + (5 – 1)z + 3 → combine like terms.
= (-13)z⁵ + (1)z³ + (4)z + 3 → simplify.
= -13z⁵ + z³ + 4z + 3
3. A metal rod with a length of (6mn-3n+1) units is divided into two sections. Find the length of the smaller half of the rod if the length of the larger part is (4mn+2n) units.
Solution:
The total length of the rod is given as (6mn-3n+1) units, while the length of the larger half of the rod is given as (4mn+2n) units.
To calculate the length of the smaller portion of the rod, subtract the length of the bigger portion from the entire length of the rod.
6mn-3n+1
(-)4mn+2n+0
(-) (-) (-)
————————-
2mn-5n+1
————————-
As a result, the length of the rod’s smaller section is (2mn-5n+1) units.
FAQs on Adding and Subtracting of Like Terms
1. How do we come up with like and unlike terms?
In an algebraic equation, similar terms exist when the variables are the same despite having distinct coefficients and exponents. In contrast, if the expression has two distinct variables, exponents, or coefficients, it is referred to as an, unlike term.
2. How Do You Add and Subtract Algebraic Expressions With Exponents?
To add or subtract algebraic expressions using exponents, there is a simple rule. For instance, 8×3+4×3=12×3.
Both the variables and their exponents must be the same so that you just need to execute the necessary operations on the coefficients, as we may combine if they have exactly the very same variables with the same absolute powers.
3. Can we add or subtract like terms while solving algebraic expressions?
Yes, we can add or subtract like terms by adding or removing their numerical coefficients.
4. What Is Algebraic Expression Subtraction in Math?
Subtraction of algebraic expressions necessitates classifying the terms of an algebraic expression as similar or unlike. Then all like terms are grouped together such that the simplified expression only contains, unlike terms.