Equivalent Expressions Flashcards

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

Answer: x² + 4xy + 4y²

Using (a+b)²=a²+2ab+b²: a=x, b=2y → x²+2(x)(2y)+(2y)² = x²+4xy+4y².

Which expression is equivalent to (x³ − x) / x?

Answer: x² − 1

Divide each term by x: x³/x = x², (−x)/x = −1; result is x²−1.

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

Answer: All of the above

Factor out 4(x+2): 4(x+2)[−(x+2)+1] = 4(x+2)(−x−1); this equals −4(x+2)(x+1), so all listed are equivalent.

Which of the following is equivalent to (a²b − ab²) / ab?

Answer: a − b

Factor numerator: ab(a−b); divide by ab to get a−b.

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

Answer: 25x² − 16

Difference of squares: (5x)²−4² = 25x²−16.

Which of the following is equivalent to (8x³ + 1) / (2x + 1)?

Answer: 4x² − 2x + 1

Sum of cubes: (2x)³+1³ = (2x+1)(4x²−2x+1); divide by (2x+1) to get 4x²−2x+1.

Which of the following is equivalent to 2x³ − 2x?

Answer: All of the above

Factor: 2x(x²−1) = 2x(x−1)(x+1); the first two listed forms represent the same expression.