8. Combine like terms to simplify 3a2b - 2ab2 + 7a2b + 5ab2

In this expression, 3a2b and 7a2b are like terms, as are -2ab2 and 5ab2. Combining them gives: (3a2b + 7a2b) + (-2ab2 + 5ab2) = 10a2b + 3ab2

Combine Like Terms Calculator: Simplify Algebraic Expressions

Latest Updates

Book Free Demo :

One-to-One Learning - Any Topic, Any Time

How to Combine Like Terms in Algebra – Methods, Steps & Examples

Combine Like Terms Calculator – Free Algebra Simplification Tool | Vedantu

Combine Like Terms Calculator

What is Combine Like Terms Calculator?

Combine Like Terms Calculator is a free tool that takes any algebraic expression and instantly simplifies it by grouping and combining terms with the same variables and powers. In algebra, "like terms" are terms that have identical variables raised to identical exponents but may have different numerical coefficients. This calculator helps students quickly rewrite expressions such as 7x + 2y + 3x + 4y as 10x + 6y, making algebra homework or exam preparation easier and faster.

Formula or Logic Behind Combine Like Terms Calculator

The main logic is:

Identify like terms: These have the same variables with the same exponents (e.g., 3x and 5x, or 2xy and 7yx—order does not matter).
Group like terms together.
Add or subtract their coefficients while keeping variables unchanged.

For example, the general formula is: ax + bx = (a+b)x. Constants (numbers without variables) are also treated as like terms with each other.

Examples of Combining Like Terms

Input Expression	Like Terms Grouped	Result
4x + 5x	(4x + 5x)	9x
7x + 2y + 3x + 4y	(7x + 3x) + (2y + 4y)	10x + 6y
2xy + 5yx + 3y	(2xy + 5yx) + (3y)	7xy + 3y
-7 - x + 5x + 12 - 6x	(-x + 5x - 6x) + (-7 + 12)	-2x + 5
3a²b - 2ab² + 7a²b	(3a²b + 7a²b) - 2ab²	10a²b - 2ab²

Steps to Use the Combine Like Terms Calculator

Enter your algebraic expression into the input box (e.g., 7x+2y+3x+4y).
Click on the 'Calculate' button.
Get instant results with step-by-step explanation shown below the calculator.

Why Use Vedantu’s Combine Like Terms Calculator?

Vedantu’s Combine Like Terms Calculator is trusted by millions of students for its accuracy, mobile-friendly design, and instant algebraic simplification. It helps you check your answers, understand the combining process, and saves precious time during studies or homework. The tool is verified by expert math educators and aligns with typical school and competitive exam standards.

Real-life Applications of Combine Like Terms

Combining like terms is used regularly while solving algebra problems in academics, simplifying equations in science and engineering, optimizing budgets or invoices with grouped costs, preparing for entrance exams, and even in fields like data science where algebraic manipulation is vital. With this calculator, you can check homework, practice for CBSE/ICSE/NCERT exams, and boost your confidence in core algebra concepts.

For more learning, explore topics like Linear Equations, Polynomials, and Like Terms in Algebra.

For quick reference, check out related calculators such as the HCF Calculator and Prime Numbers Tool.

FAQs on Combine Like Terms Calculator: Simplify Algebraic Expressions

1. What does combining like terms mean?

Combining like terms simplifies algebraic expressions by adding or subtracting terms with the same variables and exponents. It's a fundamental algebraic operation used to solve equations and simplify complex expressions. The process involves identifying like terms, then adding or subtracting their coefficients while keeping the variable and exponent unchanged.

2. How do you combine like terms step-by-step?

First, identify terms with the same variables raised to the same powers. These are your "like terms." Second, add or subtract the coefficients (the numbers in front of the variables) of the like terms. Third, keep the variable and exponent the same in the simplified expression. For example, 3x + 5x - 2x = (3 + 5 - 2)x = 6x.

3. What are some examples of like terms?

Like terms share the same variables and exponents. Here are some examples:

3x and 5x
2y² and -4y²
7ab and -2ab
1/2xy and 3xy

Note that 2x and 2x² are NOT like terms because their exponents differ.

4. Are 14xy and 42yx like terms?

Yes, 14xy and 42yx are like terms. The order of the variables does not matter; the important thing is that they have the same variables raised to the same powers. Thus, 14xy + 42yx = 56xy

5. What is the formula for combining like terms?

There isn't one single formula, but a general principle. If you have terms of the form ax and bx (where 'a' and 'b' are coefficients and 'x' is the variable), then combining them gives (a + b)x. This extends to multiple terms and different variables as well.

6. What is 7x + 2y + 3x + 4y combining like terms?

Combining like terms in the expression 7x + 2y + 3x + 4y involves grouping the 'x' terms together and the 'y' terms together. This gives (7x + 3x) + (2y + 4y) = 10x + 6y.

7. How to combine like terms with exponents?

The same principle applies when combining like terms with exponents. You only combine terms that have identical variables raised to the same powers. For example, 3x² + 5x² = 8x², but 3x² and 5x cannot be combined.

8. Combine like terms to simplify 3a²b - 2ab² + 7a²b + 5ab²

In this expression, 3a²b and 7a²b are like terms, as are -2ab² and 5ab². Combining them gives: (3a²b + 7a²b) + (-2ab² + 5ab²) = 10a²b + 3ab²

9. What are the common mistakes when combining like terms?

Common mistakes include: Adding or subtracting exponents when you should only be adding or subtracting coefficients; incorrectly identifying like terms (e.g., confusing x and x²); and making arithmetic errors when calculating coefficients. Careful attention to detail and step-by-step calculation is key.

10. Why is combining like terms important in algebra?

Combining like terms is crucial for simplifying algebraic expressions, making them easier to work with. This simplification is essential for solving equations, understanding relationships between variables, and performing more complex algebraic operations.

11. Can you combine unlike terms?

No, unlike terms cannot be combined. Unlike terms have different variables or the same variables raised to different powers. For example, you cannot combine 3x and 4y or 2x² and 5x.

12. What is the difference between simplifying expressions and combining like terms?

Combining like terms is a *part* of simplifying expressions. Simplifying expressions involves a broader range of techniques including using the distributive property, factoring, and other algebraic manipulations. Combining like terms is one of these steps in simplifying more complex expressions.