Printable pre-algebra, algebra and geometry worksheets

Algebraic Expressions Worksheets Generator

Make printable practice on simplifying algebraic expressions – combining like terms, distributing, factoring out the GCF and evaluating – with an answer key.

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This free algebraic expressions worksheet generator creates printable practice sheets for simplifying expressions, with an optional answer key. It runs in your web browser with no sign-up, and the problems are made on your own device, so nothing is uploaded. Choose the problem types you need, such as combining like terms or the distributive property, and the sheet appears in a preview on the right.

Other types cover factoring out the GCF, evaluating expressions, terms and coefficients, and equivalent expressions. It suits anyone looking for simplifying algebraic expressions worksheets with answers, whether you are a teacher preparing class work or a student practising at home. If you are looking for an adding like terms worksheet, tick only the combining like terms type. Everything you make here is free to use in class or in products you sell, such as Teachers Pay Teachers resources, Etsy printables or KDP workbooks.

Algebraic expressions worksheets example

How to use the Algebraic Expressions Worksheet Generator

  1. Under Problem types, tick one or more boxes. The page opens with Combining like terms and Distribute and combine like terms already ticked.
  2. Under Difficulty, choose Easy, Medium or Hard.
  3. Under Number of problems, pick a number from 6 to 30.
  4. Open More options if you want to change the layout. Set Columns (Automatic, 1, 2 or 3), Paper size (Letter or A4), and a Worksheet title. Tick Name and date line if students should write their name and date on the sheet.
  5. Leave Answer key on a separate page ticked to include a key, or untick it to leave the key off.
  6. Check the preview on the right. It shows the sheet as it will print.
  7. Click Show answers to display each answer under its problem in the preview. Click again to hide them.
  8. Click New worksheet for a fresh random set with the same settings, or click Print / Save as PDF to open the print dialog.

When you tick several problem types, the problems are shared out evenly and grouped by type, each group with its own one-line instruction. Problems are numbered 1 to N across the sheet, and no problem repeats. Copy link saves a link that reopens exactly the same worksheet. Settings are remembered in this browser for your next visit, unless you open a shared link, which uses that link’s settings. The tool works on phones and tablets, but printing needs a printer or the Save as PDF option.

How do you combine like terms

To combine like terms, add or subtract their coefficients and keep the same variable part. Like terms have the same variables with the same exponents, so 3x and −5x are like terms, and so are 2xy and xy, but x and x² are not.

An expression is a set of terms separated by + and −. The number in front of a variable is its coefficient, and a term without a variable is a constant. In 8x − 6 + 8 + 5x, group the x-terms and the constants separately: 8x + 5x = 13x and −6 + 8 = 2, so the result is 13x + 2.

How do you use the distributive property and combine like terms

Use the distributive property to multiply the number outside a bracket by every term inside it: a(b + c) = ab + ac. Then combine like terms. For example, 3(2x − 4) − 5x + 7 = 6x − 12 − 5x + 7 = x − 5.

Watch the signs when you subtract a group. The minus sign changes every term inside the bracket, so −3(2x − 1) = −6x + 3, not −6x − 3. The distributive property also works in reverse, which is called factoring out the GCF: 12x + 18 = 6(2x + 3).

How do you simplify expressions with two variables?

Treat each variable part as its own kind of term. x, y, xy, x² and y² are all different, so only terms with exactly the same letters and exponents combine. When a whole group is subtracted, change the sign of every term inside it first.

A Hard problem from the generator is (5x² + 4xy − 4y²) − (−2xy − y² + 5y). Removing the brackets gives 5x² + 4xy − 4y² + 2xy + y² − 5y. Then 4xy + 2xy = 6xy and −4y² + y² = −3y², while 5x² and −5y have no partners. The simplified answer is 5x² + 6xy − 3y² − 5y. An easy check is to substitute a small value such as x = 1 and y = 2 into the original and the answer; both give the same number when the work is right.

Sample problems from this generator

  1. 8y − 2x − 3y − 7x Answer: −9x + 5y
  2. −2x − y − x + 4y Answer: −3x + 3y
  3. 7x + 4(x + 2) − 7 Answer: 11x + 1
  4. 6 + 6x + 5(−3x + 5) Answer: −9x + 31

Frequently asked questions

Is there an answer key?

Yes. The answer key is on a separate page by default, and it starts after the worksheet when you print. It lists every problem number with its answer in simplest form.

What are terms, coefficients and constants?

Terms are the parts of an expression separated by + and −. A coefficient is the number in front of a variable, and a constant is a term with no variable. In 3p − 4, the terms are 3p and −4, the coefficient is 3, and the constant is −4.

How do you simplify algebraic expressions?

Distribute any brackets first, then combine like terms, and check that no like terms are left. For example, 6(x + 1) + 3x = 6x + 6 + 3x = 9x + 6.

How do I check whether two expressions are equivalent?

Simplify both expressions and compare the results. Two expressions are equivalent when they give the same value for every value of the variable. If they differ, the answer key shows a value of x where they give different results.

What does a Hard combining like terms problem look like?

A Hard example from the generator is −9y − 4 + 7y + 3x + 8x − 12. Combine the y-terms (−9y + 7y = −2y), the x-terms (3x + 8x = 11x), and the constants (−4 − 12 = −16) to get 11x − 2y − 16.

Can I sell algebraic expressions worksheets made with this generator?

Yes. Everything you make here is royalty-free for personal, classroom and commercial use, including Teachers Pay Teachers, Etsy printables, KDP workbooks and print-on-demand products. No credit is required. The only thing you may not do is copy the generator or the site itself to run a competing service. See the terms.