Equation Expander and Like-Terms Combiner

Expand a polynomial expression—or both sides of one equation—and combine like powers of x. Your input stays in your browser and is never uploaded or stored.

See the distributed terms, coefficient groups, exact simplified form, term count, and polynomial degree.

Enter an expression or equation

2(x + 3) + x − 4 + 2x

Use x, numbers, + − * /, parentheses, powers 0–12, and at most one =. Implicit multiplication such as 3x and (x+1)(x−2) is accepted.

Input rules and scope

Coefficients may be integers, finite decimals, or fractions. Division is allowed only by a nonzero constant. This tool expands one-variable polynomials; it does not accept other variables, roots, functions, negative powers, or division by an expression containing x. An equation is simplified on each side, not solved.

Try an example

Simplified result

Expanded and combined
5x + 2
Equivalent polynomial expression
Expanded terms2x + 6 + x − 4 + 2x
Like-term groupsx: 2 + 1 + 2 = 5; constants: 6 − 4 = 2
Degree1
Nonzero terms2

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Step-by-step expansion

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How to expand and combine like terms

1. Apply distribution

Multiply the factor outside parentheses by every term inside: a(b+c)=ab+ac. For two polynomials, multiply every term in the first by every term in the second.

2. Identify variable parts

Terms are alike only when their variable parts match exactly. 4x² and −x² are like terms; 4x² and 4x are not.

3. Add coefficients

Keep the shared variable part and add only its numerical coefficients: 4x²−x²=(4−1)x²=3x².

4. Write standard form

List nonzero terms from the greatest exponent to the constant. Terms whose coefficients sum to zero disappear.

Distributive property

a(b + c) = ab + ac

For example, 2(x+3)+x−4+2x expands to 2x+6+x−4+2x. Grouping gives (2+1+2)x+(6−4), so the simplified form is 5x+2.

Expansion examples

Single distribution

3(x+4)−2x+5 = 3x+12−2x+5 = x+17.

Product of binomials

(x+2)(x−3) = x²−3x+2x−6 = x²−x−6.

Terms cancel

−(x−2)(x+2)+x² = −x²+4+x² = 4.

Equation simplification

2(x+3)=x+x+6 becomes 2x+6=2x+6. The tool preserves both sides and does not solve for x.

Exact arithmetic, privacy, and limits

All parsing, distribution, coefficient addition, and output checks run locally using reduced BigInt fractions. Finite decimals are converted to exact fractions rather than rounded binary floating-point values.

The calculator supports one variable, degree 12, up to 500 distributed terms, and numeric literals up to 18 digits. These limits prevent an expression such as a deeply nested high power from exhausting the browser. The tool simplifies polynomial form only; it does not factor, solve, cancel variable denominators, or decide whether an equation is true for every value. Last reviewed: 4 August 2026.

Expanding and combining FAQs

What are like terms?

Like terms have the same variable raised to the same power. Their coefficients may differ. Constants are also like terms with one another.

How do I expand parentheses?

Use the distributive property. Multiply each term in one factor by every term in the other factor, then group matching powers.

Can the calculator simplify both sides of an equation?

Yes. Use one equals sign. Each side is expanded and combined independently; the calculator does not move terms or solve the equation.

Can I enter implicit multiplication?

Yes. Entries such as 3x, 2(x+1), and (x+1)(x−1) are interpreted as multiplication.

Why can’t unlike terms be combined?

Their variable parts represent different quantities. For example, x² and x cannot share one coefficient, so 3x²+2x is already combined.

Does the tool round decimal coefficients?

No. A finite decimal such as 0.125 is stored exactly as 1/8, then reduced and displayed as an exact fraction where needed.

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