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Advanced MathMediumIsolating the cross term

Advanced Math practice question

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

  1. A. 2abCorrect
  2. B. ab
  3. C. 0
  4. D. 2a² + 2b²

Answer: A. 2ab

(a + b)² = a² + 2ab + b². Subtracting a² + b² leaves 2ab.

Why the other answers are wrong

B. ab
The cross term in (a + b)² is 2ab, not ab.
C. 0
(a + b)² is not the same as a² + b²; the difference is the cross term 2ab.
D. 2a² + 2b²
2a² + 2b² adds the squares instead of cancelling them.

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