Simplify by Combining Like Terms Calculator

Simplify expressions, group variables, and verify each algebraic term today. Export results for clean records. Clear steps help students avoid sign mistakes during practice.

Calculator

Examples: 4x + 7 - 2x + 3y - y - 5 or 2(x + 3) - 4x.

Example Data Table

Expression Like groups Simplified result
4x + 7 - 2x + 3y - y - 5 x, y, constant 2x + 2y + 2
3a^2 + 5a - a^2 + 9 - 4a a^2, a, constant 2a^2 + a + 9
2(x + 3) - 4x + 1 x, constant -2x + 7

Formula Used

Like terms share the same variable part and the same powers. The calculator uses this rule:

aM + bM = (a + b)M

Here, M is the matching variable part. The values a and b are coefficients. Constants are grouped with constants. Terms with different powers stay separate. For example, x and x^2 are not like terms.

How to Use This Calculator

Enter the expression in the text box. Pick the result order, decimal precision, case rule, and variable reading rule. Press the simplify button. The answer will appear below the header and above the form. Review the group table. Then download a CSV or PDF copy if needed.

Why Combine Like Terms?

Combining like terms is a basic algebra step. It makes long expressions easier to read. Like terms have the same variable part. The variables must also have the same powers. For example, 3x and 7x are like terms. The terms 3x and 3x^2 are not like terms. Their powers are different.

What This Tool Checks

This calculator reads constants, variables, signs, powers, products, and simple brackets. It groups matching variable parts. Then it adds their coefficients. It can also expand products such as 2(x + 3). This helps when an expression has hidden like terms. The result is shown with clear steps. You can compare each group before using the final answer.

Why Steps Matter

Steps are useful because many errors come from signs. A negative sign can change the whole expression. The calculator keeps signed coefficients in each group. It also removes zero terms after combining. This keeps the final expression neat. Students can use the step table to see why a term stayed, changed, or disappeared.

Reading the Result

The main answer shows the simplified expression first. Summary values follow it. These include total groups, removed zero groups, and polynomial degree. The group table shows every normalized variable part. It also shows the coefficient sum. This makes review simple. If a group has a zero coefficient, it will not appear in the final expression. That saves time during careful checking.

Practical Uses

Use this calculator for homework checks, lesson examples, worksheets, and quick review. It can help with linear expressions, polynomial expressions, and expressions with several variables. It also helps teachers create answer keys. The CSV export is useful for records. The PDF export is helpful for printing or sharing.

Good Input Habits

Enter multiplication with a star when needed. Write 2*x*y when you mean separate variables. Use powers such as x^2 or y^3. Parentheses are supported for many common expressions. Avoid division by variable expressions. Division works best when the divisor is a number.

Final Note

The simplified answer is only as clear as the original expression. Use standard algebra notation. Check each term before submitting. Then review the groups and steps. This will make combining like terms faster, cleaner, and more reliable.

FAQs

What are like terms?

Like terms have the same variable part and the same powers. Their coefficients may be different. For example, 6x and -2x are like terms. The terms 6x and 6x^2 are not like terms.

Can this calculator handle parentheses?

Yes, it can handle many common parentheses. It can expand simple products such as 2(x + 3). It also supports nested parentheses when the expression follows standard operator rules.

Does it support powers?

Yes. Use the caret symbol for powers, such as x^2 or y^3. Whole number powers from 0 through 8 are supported for expanded expressions.

Can I use more than one variable?

Yes. You can use expressions with x, y, a, b, or other letters. Choose whether xy should mean x times y or one variable named xy.

Why did two terms not combine?

They likely have different variable parts or powers. For example, x, x^2, and xy are different groups. Only matching variable parts combine.

Can I divide terms?

Division is supported when the divisor is numeric. Division by an expression with variables is not supported here. Rewrite that expression before simplifying.

What does decimal precision change?

Decimal precision controls how many digits appear after calculation. It affects displayed answers and exports. It does not change the algebraic grouping rule.

What do the downloads include?

The CSV and PDF downloads include the original expression, simplified answer, degree, group count, and combined coefficients. Use them for records 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.