Simplify Calculator

Type an expression to simplify it step by step: expanding brackets and combining like terms (3(x − 2) + 4(2x + 1) = 11x − 2), cancelling factors in algebraic fractions such as (x² − 9)/(x² + 5x + 6), and applying the laws of exponents and roots – √72 = 6√2.

What “simplify” means here

• Brackets are multiplied out (the distributive property) and like terms – terms with the same letters and powers – are combined: 3x - 6 + 8x + 4 = 11x - 2.
• Rational expressions are factored top and bottom and common factors cancelled: \frac{x^2 - 9}{x^2 + 5x + 6} = \frac{(x + 3)(x - 3)}{(x + 3)(x + 2)} = \frac{x - 3}{x + 2}. Only whole factors cancel, never single terms.
• Sums of fractions are put over the lowest common denominator and combined.
• Roots lose their square factors and like roots are added: \sqrt{50} + \sqrt{18} = 5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}.
• Numbers are worked out in the order of operations, with exact fractions.

Order of operations

Brackets first, then powers and roots, then multiplication and division from left to right, then addition and subtraction from left to right (PEMDAS / BODMAS). The calculator does one level per step so you can see the order:

To factor instead of expanding, use the factoring calculator; for fractions of numbers with mixed numbers, the fraction calculator.

Examples you can simplify

Select one to see every step.

• 3x + 5 - x + 2 = 2x + 7
• 2(x + 3) - 4(x - 1) = -2x + 10
• 3a^2 b - a^2 b + 4ab = 2a^{2}b + 4ab
• (2x^2 y^3)^2 = 4x^{4}y^{6}
• x/2 + x/3 = \frac{5}{6}x
• (x^2 - 9)/(x + 3) = x - 3
• (x^2 + 5x + 6)/(x^2 - 4) = \frac{x + 3}{x - 2}
• sqrt(72) = 6\sqrt{2}

Simplifying step by step: an example

Simplify 2(x + 3) - 4(x - 1):

1. Expand the brackets: 2x + 6 - 4x + 4 (−4 × −1 = +4).
2. Group like terms: (2x - 4x) + (6 + 4).
3. Combine: -2x + 10.

Laws of exponents

• x^a \cdot x^b = x^{a+b}   \dfrac{x^a}{x^b} = x^{a-b}   (x^a)^b = x^{ab}
• (xy)^a = x^a y^a   x^0 = 1   x^{-a} = \dfrac{1}{x^a}   x^{1/2} = \sqrt{x}

Mistakes that look like simplifying

• Squaring a bracket term by term: (x + 3)^2 \ne x^2 + 9. It is x^2 + 6x + 9 – the middle term 6x comes from 2 × x × 3. See it expanded.
• Splitting a root over a sum: \sqrt{9 + 16} = 5, not 3 + 4 = 7. Roots split over multiplication (\sqrt{9 \cdot 16} = 3 \cdot 4) but never over + or −.
• Cancelling terms instead of factors: in \frac{x + 6}{x + 2} nothing cancels – the x’s are terms, not factors. Factor first; only whole brackets (or numbers) that multiply the entire top and bottom cancel.
• Losing a minus sign: -(2x - 5) = -2x + 5. The minus multiplies every term in the bracket.
• Adding unlike terms: 3x + 2x^2 is already as simple as it gets – x and x² are different kinds of term.