Equivalent Expressions Flashcards

Which of the following is equivalent to (3x + 1)/(9x² − 1)?

Answer: 1/(3x − 1)

Factor denominator: 9x²−1 = (3x+1)(3x−1); cancel (3x+1) to get 1/(3x−1).

Which expression is equivalent to (a + b + c)² − a² − b² − c²?

Answer: All of the above except C

Expanding (a+b+c)² = a²+b²+c²+2ab+2ac+2bc; subtracting a²+b²+c² leaves 2ab+2ac+2bc = 2(ab+ac+bc).

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

Answer: (x + 3)(x − 1)

Factor out (x+3): (x+3)[(x−3)+2] = (x+3)(x−1).

Which of the following is equivalent to (√x + √y)(√x − √y)?

Answer: x − y

Difference of squares: (√x)²−(√y)² = x−y.

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

Answer: (x + 2)(3x − 2)

Factor (x+2): (x+2)[4x−(x+2)] = (x+2)(4x−x−2) = (x+2)(3x−2).

Which expression is equivalent to x² − 4x + 4 − 9y²?

Answer: (x − 2 − 3y)(x − 2 + 3y)

Group as (x−2)²−(3y)²; apply difference of squares: (x−2−3y)(x−2+3y).

Which of the following is equivalent to (x⁴ − 1) / (x² + 1)?

Answer: x² − 1

Factor numerator: x⁴−1 = (x²+1)(x²−1); divide by (x²+1) to get x²−1.