Addition of Algebraic Expressions

An algebraic expression is a combination of constants and variables joined by mathematical operations such as addition, subtraction, multiplication, or division. Algebraic expressions consist of variables (unknown quantities) and constants (known values)combined using mathematical operations. For example, 2x + 5y is an algebraic expression, where x and y are variables, and 2 and 5 are constants.
 

To add algebraic expressions, group the like terms and add their coefficients. For example, you cannot add 2 pens and 2 pencils because they are different items, just like unlike terms in algebra. There are two simple ways to add algebraic expressions:

• Horizontal Method 
• Column Method 

Horizontal Method of Addition of Algebraic Expressions

For the addition of algebraic expressions by the horizontal method, follow the steps given below:
Step 1: Write all expressions in one line, separated by plus signs, and use brackets if needed. 
Step 2: Arrange and group the like terms. 
Step 3: Add the coefficients of the like terms while keeping the variables unchanged. 
Step 4: Write the simplified expression so that no two terms are alike.

Example:
Add: (3x + 2y) + (5x - y + 4)
Step 1: Combine in one line:
(3x + 2y) + (5x - y + 4)
Step 2: Group like terms:
(3x + 5x) + (2y - y) + 4
Step 3: Add coefficients:
8x + y + 4
Step 4: Simplified expression:
8x + y + 4

Column Method for Addition of Algebraic Expressions

The following steps are used for adding algebraic expressions using the column method.
Step 1: Write the expressions one below the other, aligning like terms in the same column. 
Step 2: Add the coefficients of like terms in each column.
Step 3: Combine the results from all columns to get the final expression. 

Example:
Add: 
2x2 + 3x - 4y + 7
5x + 4y -3
Step 1: Arrange the terms in a column:

Step 2: Add like terms:
2x2 - no like terms.
3x + 5x = 8x
-4y + 4y = 0
7 - 3 = 4
Step 3: Final answer:
2x2 + 8x + 4
 

When adding algebraic expressions, a few simple rules make the process easier. We only add like terms and keep the variables as they are. Using some tips, we can make the calculations faster.

• The order of the variables in the like terms does not matter. For example, 3a + 5b and 7b + 4a still have like terms like a and b, even if the order is different.
• We do not write 1 as a coefficient. For example, instead of writing 1xy, we write it as xy. 
• Always combine only like terms. In 2x + 3y + 5x, we add 2x + 5x to get 7x + 3y.
• Arrange the terms in proper order before adding. This helps to see the like terms more easily.
   

The addition of algebraic expressions is used in everyday situations where we deal with quantities that have both numbers and variables. Just like we add numbers, we can add algebraic terms to find the total of similar quantities. Here are some of the real-life applications of the addition of algebraic expressions.

• Construction and Engineering: Engineers use algebra to work with things like length, width, and height when building bridges or houses. Adding algebraic expressions helps them find the total amount or size of the material needed. 
• Finance and economics: When planning budgets or checking profits, we use algebra to show income and expenses. Adding these expressions helps find the total money earned or spent over time. 
• Physics: In physics, things like speed, distance, and force are often written as algebraic expressions. Adding expressions representing speed or force helps determine the net or total value in physics calculations. 
• Shopping: When we buy different items like pencils and notebooks, their prices can be written as algebraic expressions. Adding them gives the total cost.
• Sports: In games, scores from different rounds can be shown as algebraic expressions. Adding them gives the total score of a player or team.