If you happen to be viewing the article Addition Of Algebraic Expressions, What is an Addition of Algebraic Expression?? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
Check out to gain knowledge on the Addition of Algebraic Expressions and Learn the step-by-step methods for Addition of Algebraic Expressions and enhance your math skills. Simplify complex equations with ease.
Contents
Addition Of Algebraic Expressions
Adding algebraic expressions involves combining like terms and simplifying the resulting expression. Like terms are terms that have the same variables raised to the same powers. To add algebraic expressions, follow these steps:
Step 1: Identify like terms.
Step 2: Combine the coefficients of like terms.
Step 3: Keep the variables and exponents unchanged.
Let’s go through an example:
Example: Add the following algebraic expressions:
3x^2 + 2x + 5
4x^2 + 3x – 1
Step 1: Identify like terms.
Both expressions have terms with x^2, x, and constants (terms without variables).
Step 2: Combine the coefficients of like terms.
For x^2 terms: 3x^2 + 4x^2 = 7x^2
For x terms: 2x + 3x = 5x
For constant terms: 5 – 1 = 4
Step 3: Keep the variables and exponents unchanged.
The simplified expression is: 7x^2 + 5x + 4
So, the sum of the given algebraic expressions is 7x^2 + 5x + 4.
What is the Definition of Addition of Algebraic Expressions?
In algebra, the addition of algebraic expressions is a mathematical operation that combines two or more expressions into a single expression. These expressions can contain variables, constants, and arithmetic operations such as addition (+) and subtraction (-).
The general process of adding algebraic expressions involves identifying like terms, which are terms that have the same variables raised to the same powers. Once like terms are identified, you can combine them by adding their coefficients (the numerical values in front of the variables). Terms that do not have matching variables and powers remain unchanged.
Let’s consider an example to illustrate the addition of algebraic expressions:
Example:
Add the following algebraic expressions:
3x + 2y + 5z and 2x – y – 3z
Solution:
Step 1: Identify like terms. In this example, the like terms are those that have the same variables raised to the same powers: 3x and 2x (both have ‘x’), 2y and -y (both have ‘y’), and 5z and -3z (both have ‘z’).
Step 2: Combine the coefficients of like terms. Add the coefficients of ‘x,’ ‘y,’ and ‘z’ separately:
3x + 2x = 5x
2y – y = 1y (or just ‘y’)
5z – 3z = 2z
Step 3: Write the result as a single expression: 5x + y + 2z
So, the addition of the given algebraic expressions results in 5x + y + 2z.
How can we Add Algebraic Expressions?
Adding algebraic expressions involves combining like terms and simplifying the resulting expression. To do this, follow these steps:
Step 1: Identify Like Terms
Like terms are terms that have the same variable(s) raised to the same power(s). For example, in the expression 3x + 2y – 5x + 4y, the like terms are 3x and -5x, as well as 2y and 4y.
Step 2: Combine Like Terms
Add or subtract the coefficients of the like terms to create a new expression. Keep the variable(s) unchanged. Using the example above, combining like terms gives us 3x – 5x = -2x and 2y + 4y = 6y.
Step 3: Write the Resulting Expression
Write the new expression using the combined terms. Using the results from the previous step, the simplified expression is: -2x + 6y.
Step 4: If Necessary, Rearrange the Terms
In some cases, the final expression may need to be rearranged so that it is written in standard form, where the terms are arranged in descending order of the variable’s exponent (if any). For example, -2x + 6y could be rearranged as 6y – 2x.
Let’s work through an example:
Example: Simplify the expression 4x^2 – 3y + 2x – 5x^2 + y + 7.
Step 1: Identify Like Terms
Like terms with the same variables and exponents are: 4x^2 and -5x^2, 2x and -5x, and -3y and y.
Step 2: Combine Like Terms
Combine the coefficients of the like terms: 4x^2 – 5x^2 = -x^2, 2x – 5x = -3x, and -3y + y = -2y.
Step 3: Write the Resulting Expression
The simplified expression is: -x^2 – 3x – 2y.
Step 4: Rearrange the Terms (Optional)
The expression is already in standard form, so there is no need to rearrange the terms.
Final Result: The simplified expression is -x^2 – 3x – 2y.
Methods to Solve an Addition of Algebraic Expressions
Solving an addition of algebraic expressions involves simplifying the given expression by combining like terms and performing any necessary operations. Here are the steps you can follow to solve an addition of algebraic expressions:
Step 1: Identify Like Terms
Like terms are terms that have the same variables raised to the same powers. For example, in the expression 3x + 2y + 5x – 4y, “3x” and “5x” are like terms because they both have the variable “x” raised to the power of 1, and “2y” and “-4y” are like terms because they both have the variable “y” raised to the power of 1.
Step 2: Group Like Terms
Group all the like terms together. In the example above, we can group the like terms as follows: (3x + 5x) + (2y – 4y).
Step 3: Combine Like Terms
Perform addition or subtraction on the coefficients of the like terms. In the example, we get: 8x – 2y.
Step 4: Simplify the Result
The simplified expression after combining like terms is 8x – 2y.
Example:
Solve the addition of algebraic expressions: 4a + 2b + 7a – 3b + 6c.
Step 1: Identify Like Terms
The like terms are 4a and 7a (both have “a” raised to the power of 1), and 2b and -3b (both have “b” raised to the power of 1).
Step 2: Group Like Terms
Grouping the like terms, we have: (4a + 7a) + (2b – 3b) + 6c.
Step 3: Combine Like Terms
Performing the addition or subtraction, we get: 11a – b + 6c.
Step 4: Simplify the Result
The simplified expression after combining like terms is 11a – b + 6c.
That’s it! You’ve successfully solved the addition of algebraic expressions by combining like terms and simplifying the result. Remember to be careful with signs and pay attention to the variables and their corresponding coefficients.
What is an Example of Addition of Algebraic Expressions?
Consider the following two algebraic expressions:
- Expression A: 3x + 2y
- Expression B: 5x – y
To add these two expressions together, you simply combine the like terms. Like terms are terms that have the same variable(s) raised to the same power(s).
Step 1: Identify like terms
In the expressions A and B, the like terms are the ones that involve ‘x’ and the ones that involve ‘y’. The coefficients in front of ‘x’ and ‘y’ are not like terms, so they stay unchanged when combining the expressions.
Step 2: Add the coefficients of like terms
For the ‘x’ terms:
3x + 5x = 8x
For the ‘y’ terms:
2y + (-y) = 2y – y = y
Step 3: Combine the like terms
The result of adding the two expressions is:
(3x + 2y) + (5x – y) = 8x + y
So, the sum of the algebraic expressions A and B is 8x + y.
Algebraic Expression Solved Examples
Let’s go through some examples of adding algebraic expressions step by step.
Example 1:
Add the following expressions: 3x + 2y and 2x – y.
Step 1: Combine like terms with the same variable.
(3x + 2y) + (2x – y)
Step 2: Add the coefficients of like terms.
3x + 2x = 5x
2y – y = y
Step 3: Write the simplified expression.
5x + y
Example 2:
Add the following expressions: 4a^2 – 3ab + 2b^2 and -2a^2 + 5ab – b^2.
Step 1: Combine like terms with the same variables.
(4a^2 – 3ab + 2b^2) + (-2a^2 + 5ab – b^2)
Step 2: Add the coefficients of like terms.
4a^2 – 2a^2 = 2a^2
-3ab + 5ab = 2ab
2b^2 – b^2 = b^2
Step 3: Write the simplified expression.
2a^2 + 2ab + b^2
Example 3:
Add the following expressions: 7x^3 – 2x^2 + 5x – 9 and 3x^3 + 4x^2 – x + 6.
Step 1: Combine like terms with the same variables.
(7x^3 – 2x^2 + 5x – 9) + (3x^3 + 4x^2 – x + 6)
Step 2: Add the coefficients of like terms.
7x^3 + 3x^3 = 10x^3
-2x^2 + 4x^2 = 2x^2
5x – x = 4x
-9 + 6 = -3
Step 3: Write the simplified expression.
10x^3 + 2x^2 + 4x – 3
These are some examples of how to add algebraic expressions. Remember to combine like terms by adding or subtracting their coefficients and keeping the variable parts unchanged.
Thank you so much for taking the time to read the article titled Addition Of Algebraic Expressions, What is an Addition of Algebraic Expression? written by Math Hello Kitty. Your support means a lot to us! We are glad that you found this article useful. If you have any feedback or thoughts, we would love to hear from you. Don’t forget to leave a comment and review on our website to help introduce it to others. Once again, we sincerely appreciate your support and thank you for being a valued reader!
Source: Math Hello Kitty
Categories: Math
