Free Algebra Worksheets With Answers
These free algebra worksheets cover writing and simplifying expressions, substitution, expanding brackets, and factoring, with every answer worked through line by line. They span grades 6 to 9, which is the stretch where algebra moves from a notation exercise to a genuine problem-solving tool. When you need to assess rather than practice, the same skills can be generated as a printable algebra test with an answer key.
Grades 6–9 · 9 free questions with worked answers · No sign-up to practise
Skills covered in these algebra worksheets
- Writing expressions from words
- Collecting like terms
- Substituting values into expressions and formulas
- Expanding single and double brackets
- Factoring out a common factor
- The laws of exponents
Free algebra practice questions with answers
Every question below includes the final answer and the steps behind it, so the sheet doubles as its own answer key. Filter by grade or difficulty to build the set you need.
- Question 1easyGrade 6
Simplify 5x + 3x − 2x.
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Answer: 6x
All three terms are like terms in x, so combine the coefficients: 5 + 3 − 2 = 6, giving 6x.
- Question 2easyGrade 6
Write an expression for 'seven more than a number n'.
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Answer: n + 7
'More than' means addition, and the unknown number is n, so the expression is n + 7.
- Question 3easyGrade 6
If x = 4, what is the value of 3x − 5?
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Answer: 7
Substitute to get 3 × 4 − 5. Multiplication first gives 12, then 12 − 5 = 7.
- Question 4mediumGrade 7
Expand 3(x + 4).
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Answer: 3x + 12
Multiply every term inside the bracket by 3: 3 × x = 3x and 3 × 4 = 12.
- Question 5mediumGrade 7
Simplify 4a + 3b − 2a + 5b.
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Answer: 2a + 8b
Group like terms: 4a − 2a = 2a and 3b + 5b = 8b. The two groups cannot be combined further.
- Question 6mediumGrade 8
Factor 6x + 15.
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Answer: 3(2x + 5)
The greatest common factor of 6 and 15 is 3. Dividing each term by 3 gives 2x and 5, so the factored form is 3(2x + 5).
- Question 7hardGrade 9
Expand and simplify (x + 3)(x + 5).
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Answer: x² + 8x + 15
Multiply each pair: x² + 5x + 3x + 15. Combining the middle terms gives x² + 8x + 15.
- Question 8hardGrade 9
Simplify 2x³ × 4x².
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Answer: 8x⁵
Multiply the coefficients: 2 × 4 = 8. Add the exponents: 3 + 2 = 5. The result is 8x⁵.
- Question 9hardGrade 9
Expand and simplify 5(2x − 1) − 3(x + 4).
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Answer: 7x − 17
First 10x − 5, then −3x − 12. The subtraction applies to both terms in the second bracket. Combining gives 7x − 17.
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Like terms and why 3x + 2 does not simplify
Students meeting algebra for the first time want every expression to collapse into a single term, so 3x + 2 gets written as 5x. Only terms with an identical variable part can be combined: 3x and 5x can, 3x and 3x² cannot, and 3x and 2 cannot. Making that boundary explicit early prevents a whole family of errors in equation solving, where a wrongly combined term quietly changes the answer.
Expanding and factoring are inverse moves
Expanding 3(x + 4) gives 3x + 12, and factoring 3x + 12 gives 3(x + 4) back. Presenting them as two halves of one operation rather than two separate chapters means students can always check their own work by reversing the step. The hard questions below deliberately pair an expansion with the matching factoring so the symmetry is visible.
Common mistakes to watch for
- Combining unlike terms, so 3x + 2 is simplified to 5x.
- Multiplying only the first term inside a bracket, so 3(x + 4) becomes 3x + 4.
- Dropping the sign when expanding a bracket that follows a subtraction.
- Reading 2x² as (2x)² and squaring the coefficient as well as the variable.