Bluebook SAT Test Equivalent Expressions 9

Question 1

Which of the following is equivalent to (x + 4)(x + 4) − 16?

Accepted Answer

x² + 8x

Answer

Expand (x+4)² = x²+8x+16, then subtract 16 to get x²+8x.

Question 2

Which expression is equivalent to (15x³ − 10x²) / (5x)?

Accepted Answer

3x² − 2x

Answer

Divide each term: 15x³/5x = 3x² and −10x²/5x = −2x, giving 3x²−2x.

Question 3

Which of the following is equivalent to (n − 7)(n + 7) + 49?

Accepted Answer

n²

Answer

Using difference of squares: (n−7)(n+7) = n²−49, then n²−49+49 = n².

Question 4

Which of the following is equivalent to 2x(3x − 1) − 3x(2x − 1)?

Accepted Answer

x

Answer

Expand: 6x²−2x − (6x²−3x) = 6x²−2x−6x²+3x = x.

Question 5

Which of the following is equivalent to (x² + 2x − 15) / (x + 5)?

Accepted Answer

x − 3

Answer

Factor the numerator as (x+5)(x−3), cancel (x+5) to get x−3.

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