Addition and Subtraction of Algebraic Expressions

Algebra relies heavily on addition and subtraction operations. Understanding how to perform these basic operations on algebraic expressions is an essential foundation for algebra.

In this article, we will discuss addition and subtraction of algebraic expressions, properties and rules related to them, and examples of how to apply these operations.

Addition of Algebraic Expressions

Simplifying Like Terms

When adding algebraic expressions, the first step is to simplify like terms. Like terms are those with the same variables and exponents.

For example, in the expression 3x + 2y + 5x, the like terms are 3x and 5x. Combining them, we get 8x. Similarly, 2y remains unchanged.

Adding Unlike Terms

Next, we address unlike terms. These are terms with different variables. When adding algebraic expressions with unlike terms, we simply group them together.

For example, in 3x + 2y + 4z, you would have 3x + 2y as one group and 4z as the other.

Combining Like and Unlike Terms

To get the final result, combine both like and unlike terms.

For example, in the expression 3x + 2y + 5x, we first simplify the like terms to get 8x. Then, we group it with the unlike term 2y to obtain 8x + 2y.

Example

Write the given algebraic expressions using an additional symbol.

(4xy – 2x^2 – 8y + 3x) + (2xy – 4x – 6yz + 3x^3) + (3y – 5x^2 – yz+ 3x^3)

Step 1: Open the brackets and multiply the signs.

4xy – 2x^2 – 8y + 3x + 2xy – 4x – 6yz + 3x^3 + 3y – 5x^2 – yz + 3x^3

Step 2: Now, combine the like terms.

(4xy + 2xy) + (-2x^2 – 5x^2) + (-8y+ 3y) + (3x – 4x) + (-6yz- yz) + (3x^3 + 3x^3)

Step 3: Add the coefficients. Keep the variables and exponents on the variables the same.

6xy – 7x^2 – 5y – x – 7yz + 6x^3

Subtraction of Algebraic Expressions

Subtracting algebraic expressions follows a similar process to addition. You need to simplify like terms and group unlike terms together before performing the subtraction.

Example

Subtract 2x^2y – 3x^2 – 4zy + 6 from 5y^3 + 4x^2y – 3x^2 – 8zy + 10x^3

Step 1: Write the given algebraic expressions using an additional symbol.

(5y^3 + 4x^2y – 3x^2 – 8zy + 10x^3) – (2x^2y – 3x^2 – 4zy + 6)

Step 2: Open the brackets and multiply the signs.

5y^3 + 4x^2y – 3x^2 – 8zy + 10x^3 – 2x^2y + 3x^2 + 4zy – 6

Step 3: Now, combine the like terms.

5y^3 + (4x^2y – 2x^2y) + (-3x^2 + 3x^2) + (-8zy + 4zy) + (10x^3 – 6)

Step 4: Add the coefficients. Keep the variables and exponents on the variables the same.

5y^3 + 2x^2y + 0 – 4zy + 10x^3 – 6

5y^3 + 2x^2y – 4zy + 10x^3 – 6