by Yogi P - September 20, 2023

Addition and Subtraction of Algebraic Expressions

Addition and subtraction of algebraic expressions is a basic process used to manipulate equations and calculate the value of certain types of equations. Algebraic expressions are mathematical equations which involve unknown numbers or variables.

How to Add and Subtract Algebraic Expressions?

In order to add two algebraic expressions, one must first identify the common terms in the two expressions. The common terms can then be combined and the total value of the combined term can then be determined. The same is true when subtracting two expressions.

Once the common terms are identified, they can be subtracted from each other to determine the total value.

To add and subtract algebraic expressions, we need to combine the like terms. Like terms are terms that have the same variables and exponents.

For example, the terms 2x² and 3x² are like terms, but the terms 2x² and 3x are not like terms.

To add like terms, we simply add the coefficients.

For example, 2x² + 3x² = 5x².

To subtract like terms, we subtract the coefficients.

For example, 2x² − 3x² = −x²

If an algebraic expression has more than one term, we can use the following steps to add or subtract it:

Rewrite the expression in a way that all of the like terms are grouped together.

Add or subtract the coefficients of the like terms.

Combine any remaining terms.

For example, to add the expressions 2x² + 3x − 5 and 4x² −2x + 10, we would first rewrite them in the following way:

(2x² + 4x²) + (3x – 2x) + (-5 + 10)

Next, we would add or subtract the coefficients of the like terms:

6x² + x + 5

Finally, we would combine the remaining terms:

6x² + x + 5

To subtract algebraic expressions, we can use the same steps, but we would subtract the coefficients of the like terms instead of adding them.

Examples of Addition and Subtraction of Algebraic Expressions

To understand the full form of addition and subtraction of algebraic expressions, let’s look at an example.

Let’s say we have two equations, x + 3y = 7 and 3x – 2y = 1

In this case, the common terms are ‘x’ and ‘y’. We can then combine the terms to determine the total value of the equation.

Thus, 4x + y = 8

Similarly, if we wanted to subtract the two equations, we would subtract the common terms to get 5x – 3y = 6

Here are some examples of adding and subtracting algebraic expressions:

Addition algebraic expressions

(2x + 3) + (x + 5) = 3x + 8

Subtraction algebraic expressions

(2x + 3) – (x + 5) = x – 2

More complex example:

(2x² + 3x – 5) + (4x² – 2x + 10) = 6x² + x + 5

Importance of Adding and Subtracting Algebraic Expressions

Addition and subtraction of algebraic expressions are important tools when solving equations and determining the values of unknown numbers or variables. These operations are also fundamental to algebra, as they enable equations to be manipulated and problem-solving to be made easier.

Addition and subtraction of algebraic expressions form the cornerstone of the more complex operations of multiplication and division of algebraic expressions.

FAQs on addition and subtraction of algebraic expressions

What are like terms?

Like terms are terms that have the same variables and exponents. For example, the terms 2x² and 3x² are like terms, but the terms 2x² and 3x are not like terms.

How do I add like terms?

To add like terms, simply add the coefficients. For example, 2x² + 3x² = 5x²

How do I subtract like terms?

To subtract like terms, subtract the coefficients. For example, 2x² − 3x² = −x²

How do I add or subtract algebraic expressions with more than one term?

To add or subtract algebraic expressions with more than one term, follow these steps:

Rewrite the expression in a way that all of the like terms are grouped together.

Add or subtract the coefficients of the like terms.

Combine any remaining terms.

Here is an example:

(2x² + 3x – 5) + (4x² – 2x + 10) = 6x² + x + 5

What are some common mistakes to avoid when adding and subtracting algebraic expressions?

Some common mistakes to avoid when adding and subtracting algebraic expressions include:

• Not grouping like terms together before adding or subtracting.
• Adding or subtracting the exponents instead of the coefficients of like terms.
• Forgetting to combine any remaining terms after adding or subtracting the like terms.