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Quizzes > Mathematics

Simplifying Expressions Practice Quiz

Quick, free quiz to simplify algebraic expressions. Instant feedback.

Editorial: Review CompletedCreated By: Steven Van BeekUpdated Aug 23, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration featuring algebraic expressions and a quiz title on teal background

This quiz helps you practice simplifying expressions by combining like terms and using the distributive property. You will get instant feedback on each question, so you can spot mistakes and build speed before a test. Need a quick warm-up? Try the evaluating expressions quiz, then follow up with the solve for x quiz.

Simplify the expression: 2x + 3x
5x
x
-x
6x
Both terms are like terms since they contain the same variable to the same power. To simplify, add the coefficients: 2 + 3 = 5, giving 5x. This is a fundamental step in combining like terms when simplifying expressions.
Simplify: 5y - 2y + y
-2y
4y
2y
3y
All terms are like terms in y, so combine coefficients: 5 - 2 + 1 = 4, yielding 4y. Recognizing like terms and adding or subtracting their coefficients is key.
Simplify the expression: 4(a + 3)
a + 12
16a + 12
4a + 12
4a + 3
Use the distributive property: multiply 4 by each term inside the parentheses. 4×a = 4a and 4×3 = 12, giving 4a + 12. This property helps expand expressions quickly.
Simplify: 6x - (2x)
4x
8x
6x
-x
Removing the parentheses doesn't change signs here since it's minus a positive term: 6x - 2x = (6 - 2)x = 4x. This is another example of combining like terms after simplifying parentheses.
Simplify the expression: 3x + 2y - x + 4y
2x + 6y
x + 6y
4x + 2y
2x + 2y
Group like terms: x-terms are 3x and -x, y-terms are 2y and 4y. Combining gives (3 - 1)x = 2x and (2 + 4)y = 6y. Always combine like-variable terms.
Expand and simplify: 2(x + 5) - 3
2x + 15
x + 7
2x + 7
2x - 2
First distribute 2: 2×x + 2×5 = 2x + 10. Then subtract 3 to get 2x + 10 - 3 = 2x + 7. Distribute before combining constants.
Simplify the expression: -2(x - 4) + 3x
x + 8
x - 8
-x + 8
-5x + 8
Distribute -2 across the parentheses: -2×x + 8 = -2x + 8. Then add 3x: (-2x + 3x) + 8 = x + 8. Combine like terms after distribution.
Combine like terms: 7a - 2 + 3a + 5
10a - 3
4a + 3
10a + 3
7a + 3
Combine a-terms: 7a + 3a = 10a, and constants: -2 + 5 = 3. The result is 10a + 3. Always group like-variable terms separately from constants.
Simplify: 3(x + 2) - 2(2x - 1)
-x + 8
-5x + 8
-x - 8
x + 4
Distribute each term: 3x + 6 - (4x - 2) = 3x + 6 - 4x + 2. Combine like terms: (3x - 4x) + (6 + 2) = -x + 8.
Simplify the expression: 4(2x - 3) + 5(x + 2)
20x - 6
9x - 6
8x + 10
13x - 2
Distribute: 8x - 12 + 5x + 10. Then combine x-terms: 8x + 5x = 13x, and constants: -12 + 10 = -2, giving 13x - 2.
Expand and simplify: (x + 2)(x - 1) - x(x - 3)
x - 2
2x + 2
x^2 + x - 2
4x - 2
First expand each product: x^2 + x - 2 minus (x^2 - 3x). Subtracting yields x^2 + x - 2 - x^2 + 3x = 4x - 2. Combine like terms carefully.
Simplify the rational expression: (3x^2 - 3x) / (3x)
x
3x(x - 1)
x - 1
3(x - 1)
Factor numerator: 3x(x - 1). Divide both factors by 3x, leaving x - 1. Simplifying rational expressions often involves factoring and canceling common factors.
Simplify: (2x^2 - 8) / (2x)
x + 4/x
x - 4/x
x - 2
x + 2/x
Factor out 2 from the numerator: 2(x^2 - 4), then divide by 2x to get (x^2 - 4)/x. Finally, split the fraction: x^2/x - 4/x = x - 4/x.
Simplify the expression: 5x(x - 2) - 2(x^2 - 3x)
3x^2 - 4x
3x^2 + x
5x^2 - 6x
7x^2 - 4x
Distribute: 5x^2 - 10x - 2x^2 + 6x = (5x^2 - 2x^2) + (-10x + 6x) = 3x^2 - 4x. Carefully apply distribution and combine like terms.
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Study Outcomes

  1. Simplify Algebraic Expressions -

    Apply combining like terms and the distributive property to rewrite expressions in their simplest form.

  2. Apply the Distributive Property -

    Expand and simplify expressions involving parentheses to master algebraic simplification practice.

  3. Identify and Combine Like Terms -

    Recognize coefficients and variables to efficiently consolidate terms and streamline expressions.

  4. Use Exponent Rules -

    Employ basic exponent rules to simplify expressions with powers and improve accuracy.

  5. Increase Speed and Accuracy -

    Develop quick problem-solving techniques to boost your performance on the simplifying expressions quiz.

  6. Evaluate Exam Readiness -

    Benefit from instant feedback to identify strengths and areas for improvement before algebra tests.

Cheat Sheet

  1. Combining Like Terms -

    Like terms share the same variable and exponent, so you can sum or subtract their coefficients (e.g., 3x + 5x = 8x). This key skill, emphasized by Khan Academy's algebra curriculum, cuts down clutter in any expression. Mnemonic: "Same base, add your face" helps you remember to combine only identical bases and powers.

  2. Mastering the Distributive Property -

    The distributive property a(b + c) = ab + ac is a cornerstone of simplify algebraic expressions and is taught widely in university algebra courses (e.g., MIT OpenCourseWare). You can break down complicated sums or factor back by reversing distribution. A quick trick: check by multiplying back to ensure you get the original form.

  3. Factoring Out the Greatest Common Factor -

    Identifying the greatest common factor (GCF) in terms like 6x + 9x² simplifies expressions by rewriting them as GCF·(rest). According to the National Council of Teachers of Mathematics, factoring accelerates algebraic simplification practice. Visualize a "factor tree" to spot shared numerical and variable factors in seconds.

  4. Handling Negative Signs and Parentheses -

    Distributing negative signs (e.g., - (x - 5) = - x + 5) often trips students up; always treat the minus as multiplying by - 1. The University of Cambridge's algebra handbook stresses carefully tracking sign changes to avoid errors. Tip: rewrite a - (b - c) as a + ( - 1)(b) + ( - 1)( - c) to see each flip clearly.

  5. Applying Exponent Rules -

    When simplifying expressions with exponents, remember x^a × x^b = x^(a+b) and (x^a)/(x^b) = x^(a - b), as detailed in the American Mathematical Society's resources. These rules let you combine or reduce power terms swiftly, crucial in any simplifying expressions quiz. A fun mnemonic is "add upstairs, subtract downstairs."

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