Like terms have the same variable part with identical exponents. For example, 3x² and -5x² are like terms, but 3x² and 3x³ are not.

How do you combine like terms?

Add the coefficients while keeping the variable part unchanged. For example, 3x² + 5x² = (3+5)x² = 8x².

What is the difference between simplifying and factoring?

Simplifying combines like terms into a sum. Factoring rewrites a sum as a product. They are opposite operations.

Why is simplification useful?

Simplified expressions are easier to evaluate, compare, and use in further calculations. It is essential for solving equations and proving identities.

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Home›Algebra Tools›Algebraic Expression Simplifier

Algebraic Expression Simplifier

Enter a polynomial to automatically combine like terms and simplify

Input Expression:

Note: Use ^ for exponents, e.g. x^2 means x², x^3 means x³

Simplification Rule

Combine like terms: axᵐ + bxᵐ = (a+b)xᵐ

Find terms with identical variable parts and add their coefficients. The variable part remains unchanged.

⚠Note: Terms with different variables or different exponents are not like terms and cannot be combined.

What is Algebraic Simplification?

Simplifying (combining like terms) is the process of adding coefficients of terms with identical variable parts to obtain the simplest polynomial form.

Like Terms

Terms with the same variable(s) and same exponents. x² and x² are like; x² and x³ are not.

Method

Add coefficients, keep variable and exponent unchanged. 3x² + 5x² = 8x², -4x + 7x = 3x.

Why Simplify

Simpler expressions are easier to evaluate, compare, and use in further algebra operations.

Parentheses

Remove parentheses first, then identify and combine like terms. Watch for sign changes after a minus sign.

💡 Example: Simplify 3x² + 5x - 2x² + 7 - x.
Combine: 3x²-2x²=x², 5x-x=4x, constant 7. Result: x² + 4x + 7.

Applications

Equation Solving Identity Proofs Function Analysis Polynomial Ops Exam Prep Competitions

FAQs about Algebraic Simplification

What are like terms?▼

Terms with the same variable part and same exponents. 3x² and -5x² are like, but 3x² and 3x³ are not.

How to combine like terms?▼

Add coefficients while keeping the variable part unchanged. 3x²+5x²=(3+5)x²=8x², -4x+7x=3x.

Simplify vs factor?▼

Simplifying combines like terms into a sum. Factoring rewrites a sum as a multiplication of factors.

Why simplify?▼

Simplified polynomials are cleaner, easier to evaluate, compare, and use in further calculations like solving equations.

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