Bluebook SAT Test Equivalent Expressions 1

Question 1

Which of the following is equivalent to (x + 3)(x − 5)?

Accepted Answer

x² − 2x − 15

Answer

Using FOIL: x² − 5x + 3x − 15 = x² − 2x − 15.

Question 2

Which expression is equivalent to 3x² − 12x?

Accepted Answer

3x(x − 4)

Answer

Factor out the GCF of 3x: 3x² − 12x = 3x(x − 4).

Question 3

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

Accepted Answer

4x² − 12x + 9

Answer

(2x − 3)² = (2x)² − 2(2x)(3) + 3² = 4x² − 12x + 9.

Question 4

Which expression is equivalent to (6x³y²)/(2x²y)?

Accepted Answer

3xy

Answer

Divide coefficients: 6/2 = 3; subtract exponents: x³⁻² = x, y²⁻¹ = y; result = 3xy.

Question 5

Which of the following is equivalent to x² − 9?

Accepted Answer

(x + 3)(x − 3)

Answer

x² − 9 = x² − 3² is a difference of squares, which factors as (x + 3)(x − 3).

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