Bluebook SAT Test Equivalent Expressions 2 — Questions and Answers
Question 1: Which of the following is equivalent to 4x² − 25?
- (2x − 5)²
- (4x − 5)(x + 5)
- (2x + 5)(2x − 5) (Correct answer)
- (2x − 25)(2x + 1)
Correct answer: (2x + 5)(2x − 5)
4x² − 25 = (2x)² − 5² is a difference of squares: (2x + 5)(2x − 5).
Question 2: Which expression is equivalent to (3x + 2)(3x − 2) + 4?
- 9x² (Correct answer)
- 9x² + 4
- 9x² + 8
- 3x²
Correct answer: 9x²
(3x + 2)(3x − 2) = 9x² − 4; adding 4: 9x² − 4 + 4 = 9x².
Question 3: Which of the following is equivalent to (x² − x − 6)/(x − 3)?
- x + 2 (Correct answer)
- x − 2
- x + 3
- x − 3
Correct answer: x + 2
Factor: x² − x − 6 = (x − 3)(x + 2); cancel (x − 3): result = x + 2.
Question 4: Which of the following is equivalent to 2(x + 3)² − 18?
- 2x² + 12x
- 2x² + 12x + 18
- 2x(x + 6) (Correct answer)
- 2x² + 6x
Correct answer: 2x(x + 6)
Expand: 2(x² + 6x + 9) − 18 = 2x² + 12x + 18 − 18 = 2x² + 12x = 2x(x + 6).
Question 5: Which expression is equivalent to (x³ − 8)/(x − 2)?
- x² + 2
- x² + 4
- x² + 2x + 4 (Correct answer)
- x² − 2x + 4
Correct answer: x² + 2x + 4
x³ − 8 = (x − 2)(x² + 2x + 4) by the difference of cubes formula; cancel (x − 2).
Question 6: Which of the following is equivalent to (2x)³?
- 2x³
- 6x³
- 8x³ (Correct answer)
- 4x³
Correct answer: 8x³
(2x)³ = 2³ · x³ = 8x³.
Question 7: Which expression is equivalent to 6x² + 7x − 3?
- (6x − 1)(x + 3)
- (3x − 1)(2x + 3) (Correct answer)
- (2x + 1)(3x − 3)
- (6x + 3)(x − 1)
Correct answer: (3x − 1)(2x + 3)
(3x − 1)(2x + 3) = 6x² + 9x − 2x − 3 = 6x² + 7x − 3 ✓.
Bluebook SAT Test Equivalent Expressions 2
Which of the following is equivalent to 4x² − 25?