Algebra solver simplify: algebra expression solver with steps

Expression solver algebra: what "simplify" means

An expression has no equals sign, so there is nothing to solve for. Simplifying means rewriting it in an equivalent form with fewer terms or a cleaner shape, for example 3(2x − 4) − 2(x + 5) becomes 4x − 22. The value stays the same for every x; only the way it is written changes. That is why the last line of each solution substitutes a number into the original and the result and checks that the two agree.

The algebra expression solver: four moves cover most problems

• Expand brackets with the distributive property, taking care with a minus sign in front.
• Combine like terms: terms with the same variable part, such as 6x and −2x.
• Factor and cancel in a fraction. Only a common factor can be cancelled, never a common term.
• Use exponent rules: multiply the powers inside a power, subtract the exponents when you divide.

How to use it

1. Type the expression, starting with the word simplify. Use ^ for powers, / for fractions and brackets for grouping.
2. Read the steps. Each one is a single move: expand, collect like terms, factor, cancel or use an exponent rule.
3. Compare the last line with yours. Equivalent forms can look different.
4. Note any value the variable cannot take; the answer keeps it.

Algebra solver simplify: worked examples step by step

Each example is the solver's own output for the problem shown, and each final answer was checked separately with a computer algebra system. Tap the link under an example to run it on the board at the top of the page.

1. Simplify 3(2x - 4) - 2(x + 5)

1. Apply the distributive property to expand both terms3*(2x) - 3*(4) - 2*(x) - 2*(5)Multiply each term inside the parentheses by the factor in front of it.
2. Multiply the constants and coefficients6x - 12 - 2x - 10Compute the products: 3 * 2x = 6x, 3 * 4 = 12, and 2 * 5 = 10.
3. Group like terms together(6x - 2x) + (-12 - 10)Rearrange the expression to place variable terms together and constant terms together.
4. Combine like terms4x - 22Subtract 2x from 6x to get 4x, and combine the constants -12 and -10 to get -22.

Answer: 4x - 22

Check: Substitute x = 0 into the original expression: 3(0 - 4) - 2(0 + 5) = 3(-4) - 2(5) = -12 - 10 = -22. Substitute x = 0 into the simplified expression: 4(0) - 22 = -22. Both results match.

Open this example on the board above →

2. Simplify (x^2 - 9)/(x^2 - 5x + 6)

1. Factor the numeratorx^2 - 9 = (x - 3)(x + 3)The numerator is a difference of two squares, a^2 - b^2 = (a - b)(a + b).
2. Factor the denominatorx^2 - 5x + 6 = (x - 2)(x - 3)Find two numbers that multiply to 6 and add to -5, which are -2 and -3.
3. Rewrite the expression with factored polynomials((x - 3)(x + 3)) / ((x - 2)(x - 3))Substitute the factored forms of the numerator and denominator into the original fraction.
4. Cancel the common factor(x + 3)/(x - 2), for x ≠ 2 and x ≠ 3Divide both numerator and denominator by the common factor (x - 3). The original denominator (x - 2)(x - 3) is zero at x = 2 and x = 3, so both values stay excluded even though the factor (x - 3) cancelled.

Answer: (x + 3)/(x - 2), x ≠ 2, x ≠ 3

Check: Choose a test value, for example x = 4: the original expression gives (4^2 - 9)/(4^2 - 5(4) + 6) = (16 - 9)/(16 - 20 + 6) = 7/2. The simplified expression gives (4 + 3)/(4 - 2) = 7/2. Both values match.

Open this example on the board above →

3. Simplify (2x^3 y^2)^2 / (4 x y^5)

1. Expand the numerator using power rules(2^2 * (x^3)^2 * (y^2)^2) / (4xy^5) = (4x^6 y^4) / (4xy^5)Apply the power of a product rule (ab)^n = a^n b^n and the power of a power rule (a^m)^n = a^(mn) to the numerator.
2. Cancel common numerical coefficients(4x^6 y^4) / (4xy^5) = (x^6 y^4) / (xy^5)Divide both numerator and denominator by 4.
3. Apply the quotient rule for exponents to x and yx^(6-1) * y^(4-5) = x^5 * y^(-1)Subtract the exponent of each variable in the denominator from the exponent in the numerator using a^m / a^n = a^(m-n).
4. Express with positive exponentsx^5 / yRewrite terms with negative exponents using the rule y^(-1) = 1/y. The original expression has x and y in the denominator (4xy^5), so x and y cannot be 0, and that stays true after simplifying.

Answer: x^5 / y (x ≠ 0, y ≠ 0)

Check: Substitute x = 2 and y = 1 into the original expression: (2(2^3)(1^2))^2 / (4(2)(1^5)) = (2*8*1)^2 / 8 = 16^2 / 8 = 256 / 8 = 32. Using the simplified form: 2^5 / 1 = 32. Both evaluate to 32, confirming the solution.

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Check a simplified expression in ten seconds

Choose an easy number such as 0, 1 or 2 and put it into the original expression and into your answer. If the two results differ, something went wrong. Avoid any value that makes a denominator zero.

Why some answers carry a restriction

Simplifying does not remove values the original could not take. In the fraction examples the original denominator contains x or y, so the answers keep x ≠ 0, y ≠ 0 or x ≠ 2, x ≠ 3.

Mistakes the steps help you catch

• Losing a minus sign when it sits in front of a bracket.
• Squaring a bracket as if (x + 3)² were x² + 9. It is x² + 6x + 9.
• Cancelling terms across a fraction bar instead of factors.

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