Combining Like Terms with Negative Coefficients and Distribution Calculator

This guide explains how to combine like terms with negative coefficients and use the distribution calculator to simplify algebraic expressions. We'll cover the rules, provide practical examples, and show you how to use our interactive tool.

What Are Like Terms?

Like terms are terms in an algebraic expression that have the same variable part. For example, in the expression 3x + 5x, both terms have the variable x, so they are like terms.

When combining like terms, you add or subtract their coefficients while keeping the variable part the same. This simplifies expressions and makes them easier to work with.

Remember: Like terms must have identical variable parts with the same exponents. For example, 2xy and -5xy are like terms, but 3x and 4y are not.

Combining Like Terms with Negative Coefficients

When combining like terms with negative coefficients, you need to carefully handle the signs. Here's how to do it:

Identify all like terms in the expression
Add or subtract their coefficients while keeping the variable part the same
Simplify the expression by combining the coefficients

Example 1: Simple Combination

Combine the terms: 7y - 3y + 2y

7y - 3y + 2y = (7 - 3 + 2)y = 6y

Example 2: With Distribution

Combine the terms: -4(2x + 3) + 5x

-4(2x + 3) + 5x = -8x - 12 + 5x = (-8x + 5x) - 12 = -3x - 12

Distribution Rules

The distributive property allows you to multiply a single term by each term inside parentheses. This is essential when combining like terms with negative coefficients.

a(b + c) = ab + ac

-a(b + c) = -ab - ac

When distributing a negative coefficient, remember to change the sign of each term inside the parentheses.

Example 3: Complex Distribution

Simplify: -2(3x - 5) + 4x - 7

-2(3x - 5) + 4x - 7 = -6x + 10 + 4x - 7 = (-6x + 4x) + (10 - 7) = -2x + 3

Using the Calculator

Our interactive calculator makes it easy to combine like terms and apply distribution rules. Simply enter your expression and click "Calculate" to see the simplified result.

How to Use the Calculator

Enter your algebraic expression in the input field
Click the "Calculate" button
View the simplified result and step-by-step solution
Use the chart to visualize the terms before and after simplification

The calculator handles both positive and negative coefficients and automatically applies the distributive property when needed.

FAQ

What happens if I enter terms that aren't like terms?: The calculator will identify that the terms cannot be combined and explain why.
Can the calculator handle fractions?: Yes, the calculator can handle fractional coefficients in your expressions.
How does the calculator simplify expressions with multiple parentheses?: The calculator applies the distributive property step by step, working from the innermost parentheses outward.
Is there a limit to the complexity of expressions I can enter?: The calculator can handle most standard algebraic expressions, but very complex expressions may require manual simplification.