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SAT Math

Equivalent Expressions

Equivalent Expressions is a skill in the Advanced Math domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

14 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

Which expression is equivalent to (3x − 4) − (x − 9)?
  1. A. 2x + 5 ✓
  2. B. 4x + 5
  3. C. 2x − 13
  4. D. 4x − 13

Correct answer: A. Distribute the negative sign: 3x − 4 − x + 9 = 2x + 5.

Which expression is equivalent to (2x − 3)(x + 5)?
  1. A. 3x − 15
  2. B. 2x² + 7x − 15 ✓
  3. C. 2x² + 7x + 15
  4. D. 2x² + 10x − 15

Correct answer: B. Using FOIL: (2x)(x) + (2x)(5) + (−3)(x) + (−3)(5) = 2x² + 10x − 3x − 15 = 2x² + 7x − 15.

The expression 6x² + kx is equivalent to 2x(3x − 8) for a constant k. What is the value of k?
  1. A. 6
  2. B. 8
  3. C. −16 ✓
  4. D. −4

Correct answer: C. Expanding 2x(3x − 8) gives 6x² − 16x, so k must equal −16 for the two expressions to match.

Which expression is equivalent to 6x² − 7x − 20?
  1. A. (2x − 5)(3x + 4) ✓
  2. B. (2x + 5)(3x − 4)
  3. C. (2x − 4)(3x + 5)
  4. D. (6x + 5)(x − 4)

Correct answer: A. Correct — expanding (2x − 5)(3x + 4) gives 6x² + 8x − 15x − 20 = 6x² − 7x − 20.

Which expression is equivalent to (x² − 9)/(x² − x − 12) for all x where the expression is defined?
  1. A. (x + 3)/(x + 4)
  2. B. (x − 3)/(x − 4) ✓
  3. C. (x − 3)/(x + 4)
  4. D. (x + 3)/(x − 4)

Correct answer: B. Correct — the numerator factors as (x − 3)(x + 3) and the denominator as (x − 4)(x + 3); the shared (x + 3) factor cancels, leaving (x − 3)/(x − 4).