Advanced MathMediumDifference of two squared binomials with a coefficient
Advanced Math practice question
Which expression is equivalent to (2x + 5)² − (2x − 5)²?
- A. 40xCorrect
- B. 0
- C. 8x² + 50
- D. 20x
Answer: A. 40x
(2x + 5)² = 4x² + 20x + 25 and (2x − 5)² = 4x² − 20x + 25. Subtracting, the 4x² and 25 cancel: 20x − (−20x) = 40x.
Why the other answers are wrong
- B. 0
- The two squares differ in their middle terms, so the difference isn't zero (try x = 1: 49 − 9 = 40).
- C. 8x² + 50
- 8x² + 50 is the SUM of the two squares, not the difference.
- D. 20x
- 20x is only half: subtracting −20x from +20x gives 40x.
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