Combining Like Terms Calculator

Combine algebra terms with organized steps and checks. Review coefficients, constants, signs, and powers clearly. Export clean summaries for homework, lessons, or practice sets.

Calculator

Example Data Table

Expression Like Groups Simplified Result
3x + 4y - x + 9 - 2y + 5 x, y, constants 2x + 2y + 14
5a^2 - 3a + 7a^2 + a - 4 a^2, a, constants 12a^2 - 2a - 4
2xy + 6yx - 3x + 8 xy, x, constants 8xy - 3x + 8

Formula Used

Like terms share the same variable pattern and powers. The calculator applies this rule:

aT + bT = (a + b)T

Here, T is the shared variable part. The values a and b are coefficients. Constants use the same rule because their variable part is empty.

How To Use This Calculator

  1. Enter an expression with plus or minus signs between terms.
  2. Use the caret symbol for powers, such as x^2.
  3. Choose precision, sorting, and display options.
  4. Press the combine button.
  5. Review the simplified answer above the form.
  6. Download the result as CSV or PDF when needed.

Combining Like Terms Made Simple

Combining like terms is a core algebra skill. It turns a long expression into a cleaner form. Like terms have the same variable part. They also have the same powers. The coefficients may be different. Constants are like terms with other constants. This calculator helps you group those parts before adding or subtracting coefficients.

Why This Calculator Helps

Manual simplification can become confusing when signs, decimals, and several variables appear together. A missed negative sign can change the whole answer. This tool separates each term, identifies its variable pattern, and adds matching coefficients. It also shows grouped totals, so learners can see the structure behind the result.

What Counts As A Like Term

The variable section must match exactly. For example, 3x and -2x are like terms. The terms 5x² and 4x are not like terms. The power is different. The terms 2xy and 7yx are like terms because the same variables are present. The calculator sorts variables into a consistent order before grouping.

Advanced Use Cases

You can enter expressions with integers, decimals, fractions, constants, and multi-variable terms. Use powers with the caret symbol. For example, type x^2 instead of x squared. Multiplication signs are optional between a coefficient and a variable. You can also choose decimal precision and case handling for variables.

Learning The Result

The simplified answer is useful, but the work behind it matters. This page lists the grouped terms and the summed coefficient for each group. That makes it easier to check homework, prepare class notes, or create practice examples. The CSV export supports spreadsheet review. The document export gives a printable summary.

Best Practice

Write expressions carefully. Place plus or minus signs between terms. Use clear exponents. Avoid parentheses unless you expand them first. After getting the answer, compare each group with the original expression. This habit builds confidence and reduces algebra mistakes.

Common Mistakes To Avoid

Do not combine terms only because they share one letter. The whole variable pattern must match. Keep subtraction signs attached to the term after them. Treat a leading minus as part of the first coefficient. Recheck zero totals because opposite terms can cancel and disappear from the final expression cleanly.

FAQs

What are like terms?

Like terms have the same variable letters and the same powers. Their coefficients can be different. For example, 7x and -2x are like terms.

Can constants be combined?

Yes. Constants have no variable part, so every constant is like another constant. Add or subtract them using their signs.

Does order of variables matter?

No. The calculator sorts variables before grouping. So 2xy and 5yx are treated as matching terms.

Can I use exponents?

Yes. Type powers with the caret symbol. Use x^2, y^3, or a^2b. Terms only combine when powers match.

Are decimals allowed?

Yes. You can enter decimals as coefficients. The precision field controls how many decimal places appear in the final grouped result.

Are fractions supported?

Simple coefficient fractions are supported, such as 1/2x or -3/4y. They are converted into decimal values for grouping.

Why did a term disappear?

A group can disappear when its combined coefficient becomes zero. Enable the zero group option to show those canceled terms.

Can this expand parentheses?

No. Expand parentheses first, then enter the expression. This keeps the tool focused on combining already visible terms.

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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.