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Quizzes > Mathematics > Algebra

Simplifying Expressions Quiz - Can You Ace It?

Dive into Algebraic Simplification Practice - Challenge Yourself Now!

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 - combining like terms and using the distributive property. Get instant feedback, spot gaps before a test, and build speed. Need a quick refresher first? See our short guide , then try the evaluating expressions practice .

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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