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Quizzes > High School Quizzes > Mathematics

Select Equivalent Expressions (50) Practice Quiz

Boost algebra confidence with focused practice questions

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting an algebraic expressions trivia quiz for middle school students.

This 20‑question quiz helps you practice equivalent expressions and decide which forms match. Each question asks you to pick the expression equal to the given one. Get quick algebra practice with combining like terms, the distributive property, and exponent rules. Use it to build speed and check gaps before a test.

Which of the following is equivalent to 2(x + 3)?
x + 6
2x + 3
2x + 6
x + 3
By applying the distributive property, you multiply 2 by both x and 3, resulting in 2x + 6. This makes 2x + 6 the equivalent expression.
What is the simplified form of 3x + 4x?
7x
x
7
12x
By combining like terms, 3x and 4x add together to form 7x. This demonstrates that the correct simplified form is 7x.
Which expression is equivalent to 5 - (2x - 3)?
2x + 8
2x - 8
8 - 2x
5 - 2x - 3
Distributing the negative sign across the parentheses gives -2x + 3, and combining 5 with 3 results in 8. Thus, 8 - 2x is the correct equivalent expression.
What is the simplified form of 4(y + 2) - 2y?
2y + 8
2y - 8
6y + 2
4y + 2
Expanding 4(y + 2) gives 4y + 8 and subtracting 2y results in 2y + 8. The calculation confirms that the equivalent expression is 2y + 8.
Which expression is equivalent to -(x - 5)?
x + 5
-x + 5
-x - 5
x - 5
Distributing the negative sign to both terms inside the parentheses changes the signs, resulting in -x + 5. This confirms that -x + 5 is equivalent to -(x - 5).
Which expression is equivalent to 2(3x - 4) + 5?
6x - 4
3x - 4
6x - 3
6x + 3
Using the distributive property, 2(3x - 4) expands to 6x - 8. Adding 5 to -8 results in 6x - 3, making it the correct equivalent expression.
Simplify the expression 3(2a + 4) - 2(3a - 2).
6a + 12
a + 16
2a + 8
16
After distributing the multiplication, the variable terms cancel each other out, leaving only constant terms which sum to 16. This shows that the expression simplifies to 16.
Which expression is equivalent to (x² - 9)/(x - 3) for x ≠ 3?
x² - 3
x - 3
x + 3
x² + 3
The numerator factors as (x - 3)(x + 3), and cancelling the common factor (x - 3) leaves the expression x + 3. This is valid for x ≠ 3.
Identify the simplified form of 4x - 2(1 - x).
6x + 2
2x + 2
6x - 2
4x - 2
Distributing the -2 results in -2 + 2x, and adding this to 4x gives 6x - 2. Therefore, 6x - 2 is the correct equivalent expression.
Simplify the expression 5(2m + 3) - m.
10m + 15
9m - 15
7m + 15
9m + 15
Expanding 5(2m + 3) yields 10m + 15, and subtracting m combines like terms to give 9m + 15. This confirms that the expression simplifies to 9m + 15.
Which of the following expressions is equivalent to -(3x - 7) after applying the distributive property?
3x + 7
3x - 7
-3x - 7
-3x + 7
Distributing the negative sign changes the signs of both terms inside the parentheses, resulting in -3x + 7. This makes -3x + 7 the correctly simplified expression.
Simplify the expression 2(3y + 5) - 3(y - 2).
3y + 16
5y + 16
3y - 16
5y + 8
Expanding both parts yields 6y + 10 and -3y + 6; combining these results in 3y + 16. This is the correct simplification of the original expression.
Simplify the expression 3(x + 2) - 2(x - 1).
x + 8
5x + 4
5x + 8
x - 8
Distributing the multiplication, you obtain 3x + 6 and -2x + 2; combining like terms leads to x + 8. Thus, the equivalent expression is x + 8.
Simplify: -2(4z - 3) + 5z.
3z - 6
-3z + 6
3z + 6
-3z - 6
Distribute -2 across (4z - 3) to get -8z + 6, then add 5z resulting in -3z + 6. This confirms the correct simplified form.
Which expression is equivalent to 2x + 6 - 3(x - 2)?
-x - 12
-x + 12
x + 12
x - 12
Expanding -3(x - 2) gives -3x + 6, and adding this to 2x + 6 combines to -x + 12. This clearly shows the equivalent expression.
Determine the simplified equivalent expression for: 4(2x - 3) - 3(2x + 5) + 7.
2x - 20
8x - 20
8x + 20
2x + 20
By expanding each term, you get 8x - 12, -6x - 15, and then add 7. Combining like terms yields 2x for the variable and -20 for the constant, resulting in 2x - 20.
Which expression is equivalent to (3x² - 12)/(x - 2) for x ≠ 2?
3(x - 2)
3(x + 2)
x + 2
x - 2
Factor the numerator as 3(x² - 4), which further factors to 3(x - 2)(x + 2). Canceling the common factor (x - 2) with the denominator leaves 3(x + 2).
Simplify the expression (2x + 3) - 2(x - 4) + 3(2 - x).
3x - 17
3x + 17
-3x + 17
-3x - 17
Distribute the coefficients across each group and then combine like terms. The x terms sum to -3x and the constant terms add up to 17, yielding the simplified result -3x + 17.
Which expression is equivalent to -[2(3y - 4) - 3(y + 2)]?
-3y + 14
-3y - 14
3y + 14
3y - 14
First, simplify the expression inside the brackets: 2(3y - 4) becomes 6y - 8 and 3(y + 2) becomes 3y + 6. Their difference is 3y - 14, and applying the outer negative sign gives -3y + 14.
Simplify the expression 3(2a - 4b) + 2(5b - 3a).
0
2b
-2b
a + b
Distributing the terms gives 6a - 12b from the first part and 10b - 6a from the second part. The a terms cancel each other and the b terms combine to -2b, which is the simplified result.
0
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Study Outcomes

  1. Analyze algebraic expressions to determine equivalence.
  2. Apply the distributive property and combine like terms to simplify expressions.
  3. Evaluate multiple forms of expressions to identify equivalent structures.
  4. Utilize instant feedback to refine problem-solving techniques.
  5. Demonstrate confidence in manipulating algebraic expressions for upcoming assessments.

Review Quiz: Equivalent Expressions of (50) Cheat Sheet

  1. Understand Equivalent Expressions - Think of equivalent expressions as algebraic twins: they look different but always give the same result. Spotting them helps you rewrite problems in the easiest form and breeze through solutions.
  2. Master the Distributive Property - The distributive property is your secret weapon for breaking down parentheses: a(b + c) = ab + ac. Use it to expand, simplify, and even factor expressions in one fell swoop.
  3. Combine Like Terms - When terms share the same variable and exponent, you can add or subtract them to simplify your expression. For example, 3x + 2x magically transforms into 5x, clearing out clutter.
  4. Apply the Commutative Property - Order doesn't matter for addition or multiplication: a + b = b + a and ab = ba. This trick lets you rearrange pieces of an expression to line up like terms for easy combining.
  5. Use the Associative Property - Grouping is just a suggestion: (a + b) + c = a + (b + c) and (ab)c = a(bc). Shuffle the brackets when you need to pair up friendly terms before tackling them.
  6. Practice Factoring - Factoring is like reverse distribution: turn x² + 5x + 6 into (x + 2)(x + 3) to reveal its building blocks. Mastering this helps you solve equations and simplify massive expressions in no time.
  7. Verify Equivalence by Substitution - A quick way to test if two expressions match is to plug in a number for the variable and compare results. If they agree every time, you've nailed their equivalence - no magic wand needed.
  8. Understand the Role of Constants - Constants are the unchanging values in an expression, like the solid ground beneath shifting variables. Recognizing and managing them correctly keeps your simplifications on point.
  9. Practice with Worksheets - Drill those skills with targeted worksheets that challenge you to spot, create, and simplify equivalent expressions. Regular practice turns complexity into second nature.
  10. Engage in Interactive Learning - Make algebra a game by exploring online quizzes, puzzles, and activities that reinforce equivalent expressions. Learning through play can boost retention and keep the fun alive.
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