Combine Like Terms Calculator

Combine algebra terms with clear grouped steps. Enter any polynomial style expression and compare totals. Export simplified work with readable examples and downloads instantly.

Calculator

Example: 3x + 5x - 2y + 7 - 4 + 6x^2 - 2x^2

Example Data Table

Expression Like Groups Simplified Result
3x + 5x - 2y + 7 - 4 x, y, constant 8x - 2y + 3
6a^2 - 2a^2 + a - 9a a^2, a 4a^2 - 8a
1/2x + 3/2x - y + 4y x, y 2x + 3y
4mn + 2nm - 8 + 3 mn, constant 6mn - 5

Formula Used

Like terms have the same variable part and the same powers.

General rule: ax^n + bx^n = (a + b)x^n

Example: 7x^2 - 3x^2 = (7 - 3)x^2 = 4x^2

Constants are combined separately. A constant has no variable part.

How to Use This Calculator

  1. Enter an expression with terms separated by plus or minus signs.
  2. Use powers like x^2 when a variable has an exponent.
  3. Select the sorting method for the final expression.
  4. Choose decimal places for fraction or decimal results.
  5. Press Calculate to view the result below the header.
  6. Use CSV or PDF buttons to download the output.

Combine Like Terms Guide

Combining like terms is a basic algebra skill. It makes long expressions shorter. It also helps you see the real structure of a problem. Like terms have the same variable part. The coefficient can be different. For example, 4x and 9x are like terms. Both include x to the first power. The terms 4x and 4x^2 are not like terms, because their powers differ.

Why This Calculator Helps

Manual simplification can feel slow when an expression has many terms. Signs, decimals, fractions, and repeated variables can also cause errors. This calculator separates each term first. Then it reads the variable part. Next, it adds coefficients inside matching groups. The final answer is shown with clean signs and sorted terms.

Common Inputs

You can enter expressions such as 3x + 5x - 2y + 7 - 4. You can also use powers, such as 6a^2 - 2a^2 + a. Multiplication marks are optional in simple terms. So 3*x and 3x are treated the same. Fractions like 1/2x are accepted. Use only letters for variables and whole numbers for powers.

Reading The Result

The simplified expression is the main result. The grouped table shows how each variable group was combined. Constants are handled as their own group. A zero coefficient group can be hidden or shown. This is useful when terms cancel each other.

Learning Benefit

The step list is useful for students. It shows the term split, the group name, and the coefficient total. This makes the process easy to check. Teachers can use the example table for classroom practice. Writers can use exports for worksheets and answer keys.

Best Practices

Keep the expression simple and clear. Put a plus or minus sign between every term. Avoid parentheses unless you expand them first. Check negative signs before calculating. When the answer looks unexpected, review the grouping table. It often reveals a missing sign or mismatched power.

Advanced Options

The case option is important. Some lessons treat X and x as different variables. Other lessons combine them. Sorting also matters. Degree sorting places larger powers first. Input order keeps the original flow. Decimal places help when fractions produce longer values. Exports make the work reusable for records, study notes, and quick reports.

FAQs

What are like terms?

Like terms have the same variables raised to the same powers. Their coefficients may be different, but the variable part must match exactly.

Can constants be combined?

Yes. Constants are terms without variables. The calculator places them in a separate group and adds or subtracts them normally.

Does order of variables matter?

No. Terms like xy and yx are treated as the same group because the variables and powers match after normalization.

Can I use powers?

Yes. Use caret notation, such as x^2 or a^3. Powers must be whole numbers for this calculator.

Can I use fractions?

Yes. Simple coefficient fractions are accepted. For example, 1/2x + 3/2x becomes 2x.

Does this expand parentheses?

No. Expand parentheses before entering the expression. This calculator focuses on grouping and adding existing like terms.

Why did a term disappear?

A term may disappear when its combined coefficient becomes zero. Enable the zero group option if you want to view canceled groups.

What do the downloads include?

The CSV and PDF downloads include the original expression, simplified result, and grouped coefficient summary for review or sharing.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.