Bluebook SAT Test Equivalent Expressions 10

Question 1

Which of the following is equivalent to x⁻¹ + x⁻²?

Accepted Answer

(x + 1) / x²

Answer

Write x⁻¹ = 1/x and x⁻² = 1/x²; common denominator x² gives (x+1)/x².

Question 2

Which expression is equivalent to √(50x⁴)?

Accepted Answer

5x²√2

Answer

√50 = 5√2 and √(x⁴) = x², so √(50x⁴) = 5x²√2.

Question 3

Which of the following is equivalent to (2a³b²)(3a²b)?

Accepted Answer

6a⁵b³

Answer

Multiply coefficients 2×3=6, add exponents: a^(3+2)=a⁵ and b^(2+1)=b³, giving 6a⁵b³.

Question 4

Which of the following is equivalent to (x + 2)³ − 8?

Accepted Answer

x³ + 6x² + 12x

Answer

Expand (x+2)³ = x³+6x²+12x+8; subtract 8 to get x³+6x²+12x, which factors as x(x²+6x+12).

Question 5

Which expression is equivalent to (9x² − 6x + 1)?

Accepted Answer

(3x − 1)²

Answer

This is a perfect square trinomial: (3x)²−2(3x)(1)+1² = (3x−1)².

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