Bluebook SAT Test Equivalent Expressions 3

Question 1

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

Accepted Answer

x²

Answer

x^(1/2) · x^(3/2) = x^(1/2 + 3/2) = x^(4/2) = x².

Question 2

Which of the following is equivalent to (a²b³)/(ab)?

Accepted Answer

ab²

Answer

a²/a = a and b³/b = b², so the result is a · b² = ab².

Question 3

Which expression is equivalent to −3(2x − 5) + 4x?

Accepted Answer

−2x + 15

Answer

−6x + 15 + 4x = −2x + 15.

Question 4

Which expression is equivalent to x² + 6x + 9?

Accepted Answer

(x + 3)²

Answer

x² + 6x + 9 fits the pattern a² + 2ab + b² = (a + b)² with a = x, b = 3.

Question 5

Which of the following is equivalent to (4x³ + 8x² − 12x)/(4x)?

Accepted Answer

x² + 2x − 3

Answer

Divide each term: 4x³/4x + 8x²/4x − 12x/4x = x² + 2x − 3.

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