Equivalent Expressions Flashcards

Which of the following is equivalent to (2x + 3)(x² − x + 4)?

Answer: 2x³ + x² + 5x + 12

Distribute: 2x·x²=2x³, 2x·(−x)=−2x², 2x·4=8x, 3·x²=3x², 3·(−x)=−3x, 3·4=12; combine: 2x³+(−2x²+3x²)+(8x−3x)+12 = 2x³+x²+5x+12.

Which expression is equivalent to 8x³ − 64?

Answer: 8(x − 2)(x² + 2x + 4)

Factor out 8: 8(x³−8) = 8(x−2)(x²+2x+4) using sum/difference of cubes.

Which of the following is equivalent to (4x² − 1) / (2x − 1)?

Answer: 2x + 1

4x²−1 = (2x−1)(2x+1); dividing by (2x−1) gives 2x+1.

Which of the following is equivalent to (3x²)⁰ · (2x)³?

Answer: 8x³

Any nonzero quantity to the 0 power equals 1, so 1·(2x)³ = 8x³.

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

Answer: 1/(x − 1)

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

Which of the following is equivalent to (a − b)² + 4ab?

Answer: (a + b)²

Expand (a−b)² = a²−2ab+b², then add 4ab: a²+2ab+b² = (a+b)².

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

Answer: x²

√x = x^(1/2); multiply x^(1/2) · x^(3/2) = x^(1/2 + 3/2) = x².