In algebra, we often encounter algebraic expressions which consist of variables, constants, and mathematical operations. Addition and subtraction are two fundamental operations that can be performed on these expressions to simplify and solve equations. Let's understand the process of adding and subtracting algebraic expressions in detail.



When adding algebraic expressions, we combine like terms by adding coefficients of similar variables. Here are the steps to follow:

Step 1: Identify the like terms, i.e., terms with the same variables raised to the same powers.
Step 2: Add the coefficients of the like terms.
Step 3: Write the sum of the coefficients with the common variable.

For example, let's add the expressions 3x + 2y + 5z and 2x - 3y + 4z:

3x + 2y + 5z
+ 2x - 3y + 4z
-----------------
(3x + 2x) + (2y - 3y) + (5z + 4z)
= 5x - y + 9z

The result of adding these two expressions is 5x - y + 9z.



Subtracting algebraic expressions follows a similar process to addition. Here are the steps to follow:

Step 1: Identify the like terms, i.e., terms with the same variables raised to the same powers.
Step 2: Subtract the coefficients of the like terms.
Step 3: Write the difference of the coefficients with the common variable.

For example, let's subtract the expressions 4x + 2y - 3z and 2x - 3y + z:

(4x + 2y - 3z)
- (2x - 3y + z)
-----------------
(4x - 2x) + (2y + 3y) + (-3z - z)
= 2x + 5y - 4z

The result of subtracting these two expressions is 2x + 5y - 4z.



In conclusion, addition and subtraction of algebraic expressions involve combining like terms by adding or subtracting their coefficients. It is essential to identify the like terms before performing the operation. By following the steps outlined above, we can simplify algebraic expressions and solve equations more efficiently. Practice and familiarity with these operations will enhance your algebraic skills and help you excel in your studies.