Simplify Combining Like Terms Calculator

Type expressions and inspect every algebra step. Merge signed coefficients across matching variables and powers. Download tables, steps, and clean simplified results for study.

Calculator

Use expanded terms, such as 3x + 2x - 4y + 5. Use ^ for powers.
Decimals, fractions, signs, products, powers
4x^2y and -2yx^2 combine
Numbers without variables combine together

Formula Used

The core rule is: aM + bM = (a + b)M. Here, M means the same variable pattern with the same powers.

Constants use the same idea. For example, 7 + 4 - 2 = 9. Terms with different powers do not combine.

For multi-variable terms, the calculator sorts variables first. That means 2ab and 3ba share the same group.

How to Use This Calculator

  1. Enter an expanded algebraic expression in the text area.
  2. Use plus and minus signs between terms.
  3. Write powers with the caret symbol, such as x^2.
  4. Choose decimal places and a sorting method.
  5. Select zero groups if you want to see cancellations.
  6. Press Calculate to view the result above the form.
  7. Use CSV or PDF download buttons to save the work.

Example Data Table

Input expression Like term groups Simplified result
3x + 2x - 7 x: 3 + 2, constant: -7 5x - 7
5a^2b - 2ba^2 + 4b a^2b: 5 - 2, b: 4 3a^2b + 4b
-x + 9 - 4x + 2 x: -1 - 4, constant: 9 + 2 -5x + 11
1/2m + 3/4m - n m: 1/2 + 3/4, n: -1 1.25m - n

About the Simplify Combining Like Terms Calculator

Why this tool helps

A combining like terms calculator helps you clean an expression without losing structure. It identifies terms that share the same variable pattern. The pattern must include the same variables. It must also include the same powers. Then the calculator adds or subtracts only the coefficients.

This page is useful when expressions become long. It can handle constants, signed terms, decimal coefficients, fractions, and products of variables. It also sorts matching groups, so the final answer is easier to read. You can review each group before trusting the result.

Where combining terms appears

Combining like terms is a core algebra skill. It appears before solving equations. It also appears in polynomial work, formulas, geometry, physics, and finance models. A small sign mistake can change the answer. A structured calculator reduces that risk by showing every coefficient group.

For example, 3x and 5x are like terms. Both contain x to the first power. Their coefficients become 8. However, 3x and 5x squared are not like terms. The powers differ, so the terms remain separate. Likewise, 2ab and 7ba are like terms here. The variables are sorted into the same signature.

Reading the output

The calculator also treats constants as their own group. Numbers with no variables combine together. If a group totals zero, it can disappear from the simplified expression. You may keep zero groups visible when checking cancellations.

The best workflow is simple. Enter the expression exactly as written. Use plus and minus signs between terms. Use the caret symbol for powers. Choose decimal places and sorting. Then calculate. Read the simplified expression first. After that, inspect the table. It shows each variable group, coefficient sum, source terms, and status.

Saving your work

The download tools support record keeping. A CSV file is helpful for spreadsheets. A PDF file is useful for worksheets and saved solutions. Both exports include the input, simplified result, and grouped coefficient details.

This calculator does not replace algebra understanding. It supports it. You still learn why terms match. You still see how coefficients combine. That makes the answer easier to explain.

For better results, avoid hidden multiplication with parentheses. Write each distributive step first. Then paste the expanded expression. This keeps the calculation focused on like term grouping, not expression expansion or equation solving inside problems.

FAQs

What are like terms?

Like terms have identical variable parts. The variables and powers must match. Only coefficients can differ. Constants are like terms with other constants.

Can this calculator handle fractions?

Yes. Enter fractions such as 1/2x or -3/4ab. The calculator converts them to numeric coefficients, combines them, and rounds using your selected precision.

Why did some terms not combine?

Terms combine only when variables and powers match exactly. For example, x and x^2 are different. So are x and xy.

Does variable order matter?

No. For products of single-letter variables, ab and ba are treated as the same variable signature. The calculator sorts variables before grouping terms.

Can I use parentheses?

This tool focuses on already expanded expressions. Expand parentheses first, then paste the resulting terms. That keeps the output clear and accurate.

What is a coefficient?

A coefficient is the number multiplying a variable part. In -7x^2y, the coefficient is -7, and the variable part is x^2y.

Why does a term disappear?

A term group disappears when its combined coefficient becomes zero. Turn on zero groups if you want to review canceled terms in the table.

What do the exports include?

The CSV and PDF files include the original expression, simplified result, term count, group count, and detailed coefficient grouping information.

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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.