Bluebook SAT Test Equivalent Expressions 2

Question 1

Which of the following is equivalent to 4x² − 25?

Accepted Answer

(2x + 5)(2x − 5)

Answer

4x² − 25 = (2x)² − 5² is a difference of squares: (2x + 5)(2x − 5).

Question 2

Which expression is equivalent to (3x + 2)(3x − 2) + 4?

Accepted Answer

9x²

Answer

(3x + 2)(3x − 2) = 9x² − 4; adding 4: 9x² − 4 + 4 = 9x².

Question 3

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

Accepted Answer

x + 2

Answer

Factor: x² − x − 6 = (x − 3)(x + 2); cancel (x − 3): result = x + 2.

Question 4

Which of the following is equivalent to 2(x + 3)² − 18?

Accepted Answer

2x(x + 6)

Answer

Expand: 2(x² + 6x + 9) − 18 = 2x² + 12x + 18 − 18 = 2x² + 12x = 2x(x + 6).

Question 5

Which expression is equivalent to (x³ − 8)/(x − 2)?

Accepted Answer

x² + 2x + 4

Answer

x³ − 8 = (x − 2)(x² + 2x + 4) by the difference of cubes formula; cancel (x − 2).

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