Combining Like Terms with Negative Coefficients Calculator

Combining like terms is a fundamental algebraic operation where terms with the same variable and exponent are combined by adding or subtracting their coefficients. When dealing with negative coefficients, special attention is needed to ensure the signs are handled correctly.

What Are Like Terms?

Like terms are algebraic expressions that have the same variable raised to the same power. For example, 3x and -2x are like terms because they both contain the variable x with an exponent of 1. The coefficients (3 and -2) can be different, but the variable part must be identical.

When combining like terms, you add or subtract their coefficients while keeping the variable part unchanged. This simplifies expressions and makes them easier to work with in equations and further algebraic operations.

Combining Like Terms with Negative Coefficients

When combining like terms that have negative coefficients, you must carefully handle the signs to ensure the result is accurate. The general rule is to add or subtract the coefficients while maintaining the variable part.

Formula: a·x + b·x = (a + b)·x

Where a and b are coefficients, and x is the variable.

For example, if you have -5y + 3y, you combine them as follows:

-5y + 3y = (-5 + 3)y = -2y

Notice that the negative sign is preserved in the final result. If the sum of the coefficients is negative, the result will also be negative.

How to Use the Calculator

Our calculator makes combining like terms with negative coefficients quick and easy. Simply enter the coefficients and variable for each term, then click "Calculate" to see the combined result.

Enter the coefficient for the first term (can be negative)
Enter the variable for the first term (e.g., x, y, z)
Enter the coefficient for the second term (can be negative)
Enter the same variable for the second term
Click "Calculate" to see the result

The calculator will display the combined term and show the step-by-step calculation process.

Worked Examples

Example 1: Positive and Negative Coefficients

Combine 7x - 4x:

7x - 4x = (7 - 4)x = 3x

Example 2: Both Terms Negative

Combine -2y - 5y:

-2y - 5y = (-2 - 5)y = -7y

Example 3: Different Variables

Note: The calculator will only combine terms with the same variable.

Frequently Asked Questions

Can I combine terms with different variables?: No, you can only combine like terms that have the same variable and exponent. Terms with different variables cannot be combined.
What if one coefficient is negative and the other is positive?: Subtract the smaller absolute value from the larger one, keeping the sign of the larger coefficient. For example, 5x - 3x = 2x.
How do I handle terms with coefficients of zero?: Any term with a coefficient of zero will effectively disappear when combined with another like term. For example, 4x + 0x = 4x.
Can I combine terms with different exponents?: No, terms must have the same exponent to be combined. For example, x and x² are not like terms and cannot be combined.