Bluebook SAT Test Equivalent Expressions 8

Question 1

Which of the following is equivalent to (3x + 6)/(x² + 2x)?

Accepted Answer

3/x

Answer

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?

Accepted Answer

p³ + 3p²q + 3pq² + q³

Answer

Using the binomial expansion: (p + q)³ = p³ + 3p²q + 3pq² + q³.

Question 3

Which of the following is equivalent to x² + 10x + 25 − y²?

Accepted Answer

(x + y + 5)(x − y + 5)

Answer

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))?

Accepted Answer

1

Answer

(x − 3)/(x − 3) = 1, for x ≠ 3.

Question 5

Which of the following is equivalent to 27x³ − 8?

Accepted Answer

(3x − 2)(9x² + 6x + 4)

Answer

Difference of cubes: (3x)³ − 2³ = (3x − 2)((3x)² + (3x)(2) + 4) = (3x − 2)(9x² + 6x + 4).

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