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Combining Like Terms Calculator

Simplify algebraic expressions by merging terms with identical variables and exponents. Visualizes the grouping process with color-coded steps.

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Category Math & Algebra
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About

One of the first hurdles in algebra is learning to identify "Like Terms." These are terms that share the exact same variable part, including exponents. For instance, 2x and 5x can be combined to make 7x, but 2x and 5y must remain separate. This distinction is critical for solving equations.

This calculator acts as a visual guide. Instead of just showing the final answer, it breaks down the expression, identifies which chunks belong together, and demonstrates the summation of their coefficients. This transparency helps users correct common mistakes, such as accidentally combining x2 and x.

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Formulas

The process rests on the Distributive Property of multiplication over addition:

ax + bx = (a + b)x

This rule is valid regardless of how complex x is, as long as it is identical in both terms.

Reference Data

ExpressionLike Terms?ResultRule
3x + 4xYES7xAdd coefficients
2x2 + 3xNOSameDifferent exponents
5xy − xyYES4xyxy has coeff 1
3a + 2bNOSameDifferent variables
x2y + xy2NOSameExponent mismatch

Frequently Asked Questions

Terms are "like" if they have the exact same variables raised to the exact same powers. The coefficient (the number in front) does not need to match.
Yes. Multiplication is commutative, meaning order doesn't matter. xy is mathematically identical to yx, so they can be combined.
Absolutely. Numbers without variables (like 5, -3, 10.5) are considered like terms and should always be combined into a single value.