Bluebook SAT Test Equivalent Expressions 10 — Questions and Answers
Question 1: Which of the following is equivalent to x⁻¹ + x⁻²?
- (x + 1) / x² (Correct answer)
- (x² + x) / x²
- 2x⁻³
- 1 / (x + x²)
Correct answer: (x + 1) / x²
Write x⁻¹ = 1/x and x⁻² = 1/x²; common denominator x² gives (x+1)/x².
Question 2: Which expression is equivalent to √(50x⁴)?
- 5x²√2 (Correct answer)
- 5x²
- 10x²
- 5√(2x⁴)
Correct answer: 5x²√2
√50 = 5√2 and √(x⁴) = x², so √(50x⁴) = 5x²√2.
Question 3: Which of the following is equivalent to (2a³b²)(3a²b)?
- 6a⁵b³ (Correct answer)
- 5a⁵b³
- 6a⁶b²
- 6a⁵b²
Correct answer: 6a⁵b³
Multiply coefficients 2×3=6, add exponents: a^(3+2)=a⁵ and b^(2+1)=b³, giving 6a⁵b³.
Question 4: Which of the following is equivalent to (x + 2)³ − 8?
- x³ + 6x² + 12x (Correct answer)
- x³ + 6x² + 12x + 16
- x³ + 8
- x(x² + 6x + 12)
Correct answer: x³ + 6x² + 12x
Expand (x+2)³ = x³+6x²+12x+8; subtract 8 to get x³+6x²+12x, which factors as x(x²+6x+12).
Question 5: Which expression is equivalent to (9x² − 6x + 1)?
- (3x − 1)² (Correct answer)
- (3x + 1)²
- (9x − 1)(x − 1)
- (3x − 1)(3x + 1)
Correct answer: (3x − 1)²
This is a perfect square trinomial: (3x)²−2(3x)(1)+1² = (3x−1)².
Question 6: Which of the following is equivalent to (x³ + 27) / (x + 3)?
- x² − 3x + 9 (Correct answer)
- x² + 3x + 9
- x² − 9
- (x − 3)²
Correct answer: x² − 3x + 9
Sum of cubes: x³+27 = (x+3)(x²−3x+9); divide by (x+3) to get x²−3x+9.
Question 7: Which of the following is equivalent to 5x² − 5?
- 5(x − 1)(x + 1) (Correct answer)
- 5(x − 1)²
- 5x(x − 1)
- (5x − 1)(x + 1)
Correct answer: 5(x − 1)(x + 1)
Factor out 5: 5(x²−1) = 5(x−1)(x+1) using difference of squares.
Bluebook SAT Test Equivalent Expressions 10
Which of the following is equivalent to x⁻¹ + x⁻²?