Bluebook SAT Test Equivalent Expressions 9 — Questions and Answers
Question 1: Which of the following is equivalent to (x + 4)(x + 4) − 16?
- x² + 8x (Correct answer)
- x² + 8x + 32
- x² + 16x
- x² + 8x − 16
Correct answer: x² + 8x
Expand (x+4)² = x²+8x+16, then subtract 16 to get x²+8x.
Question 2: Which expression is equivalent to (15x³ − 10x²) / (5x)?
- 3x² − 2x (Correct answer)
- 3x² − 2
- 10x² − 5x
- 3x − 2
Correct answer: 3x² − 2x
Divide each term: 15x³/5x = 3x² and −10x²/5x = −2x, giving 3x²−2x.
Question 3: Which of the following is equivalent to (n − 7)(n + 7) + 49?
- n² (Correct answer)
- n² + 49
- n² − 49
- n² + 14n
Correct answer: n²
Using difference of squares: (n−7)(n+7) = n²−49, then n²−49+49 = n².
Question 4: Which of the following is equivalent to 2x(3x − 1) − 3x(2x − 1)?
- x (Correct answer)
- −x
- 12x² − 5x
- 6x² − 5x
Correct answer: x
Expand: 6x²−2x − (6x²−3x) = 6x²−2x−6x²+3x = x.
Question 5: Which of the following is equivalent to (x² + 2x − 15) / (x + 5)?
- x − 3 (Correct answer)
- x + 3
- x − 5
- x + 5
Correct answer: x − 3
Factor the numerator as (x+5)(x−3), cancel (x+5) to get x−3.
Question 6: Which expression is equivalent to (4x + 8) / (x² + 4x + 4)?
- 4 / (x + 2) (Correct answer)
- 4 / (x − 2)
- (x + 2) / 4
- 4x / (x + 2)
Correct answer: 4 / (x + 2)
Factor: numerator = 4(x+2), denominator = (x+2)², so the ratio is 4/(x+2).
Question 7: Which of the following is equivalent to (3x − 5)² − (3x + 5)²?
- −60x (Correct answer)
- 60x
- −30x
- 0
Correct answer: −60x
Using a²−b² = (a−b)(a+b): let a = 3x−5, b = 3x+5; a−b = −10, a+b = 6x−0 = 6x, so product = −60x.
Bluebook SAT Test Equivalent Expressions 9
Which of the following is equivalent to (x + 4)(x + 4) − 16?