Bluebook SAT Test Equivalent Expressions 14

Question 1

Which of the following is equivalent to (x − 2)(x² + 2x + 4)?

Accepted Answer

x³ − 8

Answer

This is the difference of cubes factored: (x−2)(x²+2x+4) = x³−2³ = x³−8.

Question 2

Which expression is equivalent to 18x³ − 12x² + 6x?

Accepted Answer

6x(3x² − 2x + 1)

Answer

GCF is 6x; factoring out gives 6x(3x²−2x+1). The other options are incorrect or un-simplified.

Question 3

Which of the following is equivalent to (5x + 2)² − (5x − 2)²?

Accepted Answer

40x

Answer

Use a²−b² = (a+b)(a−b): a+b = (5x+2)+(5x−2)=10x, a−b = (5x+2)−(5x−2)=4; product = 40x.

Question 4

Which of the following is equivalent to (3x²y³)² / (9xy)?

Accepted Answer

x³y⁵

Answer

Numerator: (3x²y³)² = 9x⁴y⁶; divide by 9xy: 9x⁴y⁶/(9xy) = x³y⁵.

Question 5

Which expression is equivalent to (2x − 5)(2x + 5) + 25?

Accepted Answer

4x²

Answer

(2x−5)(2x+5) = 4x²−25; add 25: 4x²−25+25 = 4x².

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