Bluebook SAT Test Equivalent Expressions 16

Question 1

Which of the following is equivalent to (3x + 1)/(9x² − 1)?

Accepted Answer

1/(3x − 1)

Answer

Factor denominator: 9x²−1 = (3x+1)(3x−1); cancel (3x+1) to get 1/(3x−1).

Question 2

Which expression is equivalent to (a + b + c)² − a² − b² − c²?

Accepted Answer

All of the above except C

Answer

Expanding (a+b+c)² = a²+b²+c²+2ab+2ac+2bc; subtracting a²+b²+c² leaves 2ab+2ac+2bc = 2(ab+ac+bc).

Question 3

Which of the following is equivalent to (x − 3)(x + 3) + 2(x + 3)?

Accepted Answer

(x + 3)(x − 1)

Answer

Factor out (x+3): (x+3)[(x−3)+2] = (x+3)(x−1).

Question 4

Which of the following is equivalent to (√x + √y)(√x − √y)?

Accepted Answer

x − y

Answer

Difference of squares: (√x)²−(√y)² = x−y.

Question 5

Which of the following is equivalent to 4x(x + 2) − (x + 2)²?

Accepted Answer

(x + 2)(3x − 2)

Answer

Factor (x+2): (x+2)[4x−(x+2)] = (x+2)(4x−x−2) = (x+2)(3x−2).

Bluebook SAT Practice Test