Equivalent Expressions Flashcards

Which of the following is equivalent to 2x² + 5x − 3?

Answer: (2x − 1)(x + 3)

(2x − 1)(x + 3) = 2x² + 6x − x − 3 = 2x² + 5x − 3 ✓.

Which of the following is equivalent to ((x²y)/(z))²?

Answer: x⁴y²/z²

Apply the power to each part: (x²)² = x⁴, y² = y², z² = z²; result = x⁴y²/z².

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

Answer: (3x + 1)/3

Add numerators over common denominator: (2x − 1 + x + 2)/3 = (3x + 1)/3.

Which of the following is equivalent to (x² − 2x − 8)?

Answer: (x − 4)(x + 2)

Find two numbers that multiply to −8 and add to −2: −4 and +2; so (x − 4)(x + 2).

Which of the following is equivalent to a⁰ for any nonzero value of a?

Answer: 1

Any nonzero number raised to the power 0 equals 1, by definition of the zero exponent rule.

Which of the following is equivalent to (6x³ − 4x² + 2x)/(2x)?

Answer: 3x² − 2x + 1

Divide each term: 6x³/2x − 4x²/2x + 2x/2x = 3x² − 2x + 1.

Which of the following is equivalent to (x − 5)(x + 5) − x(x − 10)?

Answer: 10x − 25

(x² − 25) − x(x − 10) = x² − 25 − x² + 10x = 10x − 25.