Bluebook SAT Test Equivalent Expressions 8 — Questions and Answers
Question 1: Which of the following is equivalent to (3x + 6)/(x² + 2x)?
- 3/x (Correct answer)
- (3x + 6)/x
- 3/(x + 2)
- 3/(x(x+2))
Correct answer: 3/x
Factor: numerator = 3(x + 2), denominator = x(x + 2); cancel (x + 2): result = 3/x.
Question 2: Which of the following is equivalent to (p + q)³?
- p³ + q³
- p³ + 3p²q + 3pq² + q³ (Correct answer)
- p³ + 2pq + q³
- 3p + 3q
Correct answer: p³ + 3p²q + 3pq² + q³
Using the binomial expansion: (p + q)³ = p³ + 3p²q + 3pq² + q³.
Question 3: Which of the following is equivalent to x² + 10x + 25 − y²?
- (x + 5 + y)(x + 5 − y)
- (x + 5)² − y²
- (x + y + 5)(x − y + 5) (Correct answer)
- (x + 5 − y)²
Correct answer: (x + y + 5)(x − y + 5)
Group: (x + 5)² − y² = ((x + 5) + y)((x + 5) − y) = (x + y + 5)(x − y + 5).
Question 4: Which of the following is equivalent to (x/(x−3)) − (3/(x−3))?
- 1 (Correct answer)
- −1
- x − 3
- 3/(x−3)
Correct answer: 1
(x − 3)/(x − 3) = 1, for x ≠ 3.
Question 5: Which of the following is equivalent to 27x³ − 8?
- (3x − 2)(9x² + 6x + 4) (Correct answer)
- (3x − 2)³
- (3x − 2)(9x² − 12x + 4)
- (3x + 2)(9x² − 6x + 4)
Correct answer: (3x − 2)(9x² + 6x + 4)
Difference of cubes: (3x)³ − 2³ = (3x − 2)((3x)² + (3x)(2) + 4) = (3x − 2)(9x² + 6x + 4).
Question 6: Which of the following is equivalent to (x² − 6x + 9)/(x − 3)?
- x − 3 (Correct answer)
- x + 3
- (x − 3)²
- 1
Correct answer: x − 3
x² − 6x + 9 = (x − 3)²; cancel one factor of (x − 3): result = x − 3.
Question 7: Which of the following expressions is equivalent to (1 − x²)/(x² − 1)?
- 1
- −1 (Correct answer)
- 0
- x
Correct answer: −1
(1 − x²) = −(x² − 1); so (1 − x²)/(x² − 1) = −(x² − 1)/(x² − 1) = −1, for x ≠ ±1.
Bluebook SAT Test Equivalent Expressions 8
Which of the following is equivalent to (3x + 6)/(x² + 2x)?