Simplify Expressions Calculator

Reviewed by CalcMulti Editorial Team·Last updated: March 2026·← Algebra Hub

Simplifying an algebraic expression means rewriting it in its most compact, equivalent form by combining like terms, applying the distributive property, and using exponent rules. A simplified expression contains no parentheses that can be expanded, no like terms that can be merged, and no negative or fractional exponents that can be rewritten.

This calculator walks through simplification step by step: identifying like terms, collecting coefficients, expanding brackets using the distributive property or FOIL, and applying laws of exponents. Whether you are working with polynomials, rational expressions, or radicals, each reduction is shown explicitly so you can follow the logic and reproduce it by hand.

Simplification is not just cosmetic — it is a prerequisite for almost every further operation in algebra. A quadratic equation must be simplified before you can factor it or apply the quadratic formula. A rational expression must have its numerator and denominator simplified before you can cancel common factors. A trigonometric identity must be reduced before the pattern becomes visible. Skipping simplification creates errors that compound through every subsequent step, so building the habit of fully simplifying after each operation is one of the highest-leverage skills in algebra.

The most common simplification errors involve signs. Distributing a negative: −3(x − 4) becomes −3x + 12 (not −3x − 12). Subtracting an expression: 5x − (2x − 7) becomes 5x − 2x + 7 = 3x + 7 (not 3x − 7). These sign mistakes are the leading source of wrong answers in algebraic calculations. Always distribute the negative sign to every term inside the parentheses before combining like terms, and never drop the negative sign when moving a term across an equals sign.

Understanding the underlying rules — not just memorising the steps — makes simplification faster and more reliable. The distributive property a(b + c) = ab + ac is the engine behind both expansion and factoring. The commutative and associative properties let you reorder and regroup terms freely before collecting them. The laws of exponents (product rule, quotient rule, power rule, negative exponent rule) cover every situation involving powers. Once you can identify which rule applies to which part of an expression, simplification becomes a systematic process rather than a guess-and-check exercise.

Worked examples step by step: (1) Simplify 4x² + 3x − 2x² + 7 − 5x. Group like terms: (4x² − 2x²) + (3x − 5x) + 7 = 2x² − 2x + 7. Done — no further simplification possible. (2) Simplify 2(3x − 4) − 3(x + 2). Distribute: 6x − 8 − 3x − 6. Combine: (6x − 3x) + (−8 − 6) = 3x − 14. (3) Expand and simplify (2x + 3)(x − 5). FOIL: 2x·x + 2x·(−5) + 3·x + 3·(−5) = 2x² − 10x + 3x − 15 = 2x² − 7x − 15. (4) Simplify x³·x⁻² = x^(3+(−2)) = x¹ = x. These four operations — combining like terms, distributing, FOIL, and exponent rules — cover the vast majority of simplification tasks encountered in algebra courses.

Simplifying rational expressions requires an extra step: factor numerator and denominator before cancelling. Example: simplify (x² − 9)/(x² + 5x + 6). Factor: (x − 3)(x + 3) / (x + 2)(x + 3). Cancel (x + 3) from both: (x − 3)/(x + 2), restricted to x ≠ −3 (the cancelled factor creates a restriction). A common error is cancelling terms instead of factors: (x² + 5)/(x²) cannot be simplified to 1 + 5 — you can only cancel factors that multiply the entire numerator and denominator. Similarly, (x + 4)/(x + 7) cannot be simplified because x is a term (added), not a factor (multiplied).

The laws of exponents handle every power situation systematically. Product rule: xᵃ · xᵇ = x^(a+b). Quotient rule: xᵃ / xᵇ = x^(a−b). Power rule: (xᵃ)ᵇ = x^(ab). Zero exponent: x⁰ = 1 (for x ≠ 0). Negative exponent: x⁻ⁿ = 1/xⁿ. Fractional exponent: x^(m/n) = (x^m)^(1/n) = ⁿ√(xᵐ). Worked example: simplify (2x³y²)² / (4x⁵y). Apply power rule: 4x⁶y⁴ / 4x⁵y. Divide coefficients: 1. Apply quotient rule for x: x^(6−5) = x. For y: y^(4−1) = y³. Result: xy³.