Bluebook SAT Test Equivalent Expressions 1 — Questions and Answers
Question 1: Which of the following is equivalent to (x + 3)(x − 5)?
- x² − 2x − 15 (Correct answer)
- x² + 2x − 15
- x² − 8x − 15
- x² − 15
Correct answer: x² − 2x − 15
Using FOIL: x² − 5x + 3x − 15 = x² − 2x − 15.
Question 2: Which expression is equivalent to 3x² − 12x?
- 3(x² − 4)
- 3x(x − 4) (Correct answer)
- x(3x − 12)
- 3(x − 4)²
Correct answer: 3x(x − 4)
Factor out the GCF of 3x: 3x² − 12x = 3x(x − 4).
Question 3: Which of the following is equivalent to (2x − 3)²?
- 4x² − 9
- 4x² + 9
- 4x² − 6x + 9
- 4x² − 12x + 9 (Correct answer)
Correct answer: 4x² − 12x + 9
(2x − 3)² = (2x)² − 2(2x)(3) + 3² = 4x² − 12x + 9.
Question 4: Which expression is equivalent to (6x³y²)/(2x²y)?
- 3xy (Correct answer)
- 3x²y
- 4xy
- 3x/y
Correct answer: 3xy
Divide coefficients: 6/2 = 3; subtract exponents: x³⁻² = x, y²⁻¹ = y; result = 3xy.
Question 5: Which of the following is equivalent to x² − 9?
- (x − 3)²
- (x + 3)(x − 3) (Correct answer)
- (x − 9)(x + 1)
- (x − 3)(x + 9)
Correct answer: (x + 3)(x − 3)
x² − 9 = x² − 3² is a difference of squares, which factors as (x + 3)(x − 3).
Question 6: Which expression is equivalent to (x² + 5x + 6)/(x + 2)?
- x + 3 (Correct answer)
- x + 2
- x − 3
- x + 6
Correct answer: x + 3
Factor the numerator: x² + 5x + 6 = (x + 2)(x + 3); cancel (x + 2): result = x + 3.
Question 7: Which of the following is equivalent to 5(2x − 3) − 2(x + 4)?
- 8x − 23 (Correct answer)
- 8x − 7
- 12x − 7
- 8x + 7
Correct answer: 8x − 23
Distribute: 10x − 15 − 2x − 8 = 8x − 23.
Bluebook SAT Test Equivalent Expressions 1
Which of the following is equivalent to (x + 3)(x − 5)?