Bluebook SAT Test Equivalent Expressions 13

Question 1

Which of the following is equivalent to 16x² − 24x + 9?

Accepted Answer

(4x − 3)²

Answer

This is a perfect square trinomial: (4x)²−2(4x)(3)+3² = (4x−3)².

Question 2

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

Accepted Answer

1/(x − 2)

Answer

Factor denominator: x²+x−6 = (x+3)(x−2); cancel (x+3) to get 1/(x−2).

Question 3

Which expression is equivalent to 3(2x − 1)² − 3?

Accepted Answer

All of the above

Answer

Expand 3(4x²−4x+1)−3 = 12x²−12x+3−3 = 12x²−12x = 12x(x−1) = 6·2x(x−1); all are equivalent.

Question 4

Which of the following is equivalent to (x^(1/3))^6?

Accepted Answer

x²

Answer

Using the power of a power rule: (x^(1/3))^6 = x^(1/3 · 6) = x² (since 6/3 = 2).

Question 5

Which of the following is equivalent to (4x + 2)(x − 3)?

Accepted Answer

4x² − 10x − 6

Answer

FOIL: 4x·x=4x², 4x·(−3)=−12x, 2·x=2x, 2·(−3)=−6; combine: 4x²+(−12x+2x)−6 = 4x²−10x−6.

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