Bluebook SAT Test Equivalent Expressions 4 — Questions and Answers
Question 1: Which of the following is equivalent to (2x + 1)(x² − 3x + 2)?
- 2x³ − 5x² + x + 2 (Correct answer)
- 2x³ − 6x² + 4x + x² − 3x + 2
- 2x³ + x² − 3x + 2
- 2x³ − 5x² + 5x + 2
Correct answer: 2x³ − 5x² + x + 2
Expand: 2x(x² − 3x + 2) + 1(x² − 3x + 2) = 2x³ − 6x² + 4x + x² − 3x + 2 = 2x³ − 5x² + x + 2.
Question 2: If 3x² − 27 = 0, which factored form represents the left side?
- 3(x − 3)(x + 3) (Correct answer)
- 3(x − 9)(x + 3)
- 3(x − 3)²
- (3x − 9)(x + 3)
Correct answer: 3(x − 3)(x + 3)
3x² − 27 = 3(x² − 9) = 3(x − 3)(x + 3) by difference of squares.
Question 3: Which of the following is equivalent to x⁻³?
- −x³
- 1/x³ (Correct answer)
- 3/x
- x^(1/3)
Correct answer: 1/x³
A negative exponent means taking the reciprocal: x⁻³ = 1/x³.
Question 4: Which of the following is equivalent to (3x − 2)/5 + (x + 1)/5?
- (4x − 1)/5 (Correct answer)
- (4x + 1)/5
- (2x − 1)/5
- (4x − 1)/10
Correct answer: (4x − 1)/5
Same denominator: (3x − 2 + x + 1)/5 = (4x − 1)/5.
Question 5: Which expression is equivalent to (x − 4)² − (x + 4)²?
- −16x (Correct answer)
- −32x
- −16
- 32x
Correct answer: −16x
(x − 4)² − (x + 4)² = (x² − 8x + 16) − (x² + 8x + 16) = −16x.
Question 6: Which of the following is equivalent to x^(2/3)?
- ∛x² (Correct answer)
- x²/3
- 2x/3
- (√x)³
Correct answer: ∛x²
x^(2/3) = (x²)^(1/3) = ∛(x²), the cube root of x squared.
Question 7: Which of the following is equivalent to 4(x + 2)² − 4(x + 2) − 8?
- 4(x + 2)(x + 1) − 8
- 4(x + 2 − 2)(x + 2 + 1)
- 4(x + 2)(x + 1) (Correct answer)
- 4x(x + 3)
Correct answer: 4(x + 2)(x + 1)
Let u = x + 2: 4u² − 4u − 8 = 4(u² − u − 2) = 4(u − 2)(u + 1) = 4(x)(x + 3) = 4x(x + 3).
Bluebook SAT Test Equivalent Expressions 4
Which of the following is equivalent to (2x + 1)(x² − 3x + 2)?