No products in the cart.
For addition of algebraic expressions, you treat them much like standard addition, but with an extra step. You have to sort the terms into two categories like and unlike. After sorting, you simply add the like terms together and leave the unlike terms as they are.
Think of it like sorting fruit: you can add 3 apples to 2 apples to get 5 apples, but you can’t add 3 apples to 2 oranges and get “5 app-oranges.” They just stay as they are.
Table of Contents
1. The Golden Rule: Like Terms
To add expressions, you must identify Like Terms. These are terms that have the exact same variables raised to the exact same exponents.
| Term A | Term B | Status | Reason |
| $3x$ | $5x$ | Like | Same variable ($x$) |
| $2x^2$ | $7x^2$ | Like | Same variable and exponent ($x^2$) |
| $4x$ | $4y$ | Unlike | Different variables ($x$ vs $y$) |
| $5x$ | $5x^2$ | Unlike | Different exponents ($1$ vs $2$) |
2. Two Methods for Addition
There are two main ways to set up your work. Let’s use this example:
Add $(3x + 5y – 2)$ and $(2x – 2y + 7)$
2.1 Method A: The Horizontal Method
In this method, you write everything in one line, group the like terms together, and then simplify.
1. Write the sum: $(3x + 5y – 2) + (2x – 2y + 7)$
2. Group like terms: $(3x + 2x) + (5y – 2y) + (-2 + 7)$
3. Combine coefficients: $5x + 3y + 5$
2.2 Method B: The Vertical (Column) Method
This is often easier for long expressions. You line up the like terms in columns, just like multi-digit addition.
$$\begin{array}{r@{\quad}l} 3x + 5y – 2 \\ + 2x – 2y + 7 \\ \hline 5x + 3y + 5 \end{array}$$
3. Step by Step on How to Add Algebraic Expression
If you’re tackling a complex problem, follow these steps:
Step 1: Remove Parentheses. If there is a plus sign outside the parentheses, the signs of the terms inside stay exactly the same.
Step 2: Identify Like Terms. Use different colored highlighters or different underlines (like a wavy line for $x$ and a straight line for $x^2$) to spot them.
Step 3: Add the Coefficients. Only add the numbers in front. Never change the exponents when adding. (e.g., $x + x = 2x$, not $x^2$).
Step 4: Write the Final Result. Usually, we write the terms in descending order of their exponents (Standard Form).
Pro Tip: If a variable has no number in front of it (like $x$ or $y^2$), there is an invisible 1 there. So, $x + 3x$ is actually $1x + 3x = 4x$.
Example for Addition of Algebraic Expression
Problem: Add $(4a^2 + 3b – 7)$ and $(a^2 – 5b + 2)$.
1. Identify Like Terms: $(4a^2, a^2)$, $(3b, -5b)$, and $(-7, 2)$.
2. Combine $a^2$ terms: $4a^2 + 1a^2 = 5a^2$
3. Combine $b$ terms: $3b + (-5b) = -2b$
4. Combine constants: $-7 + 2 = -5$
5. Final Answer: $5a^2 – 2b – 5$
Check out our full chapter with all the concepts here : Algebra Basics
