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In a visual model, two strips ab and ab are removed from an a² square, but the corner b² is removed twice. What is the correct remaining area?

Answer and explanation

Correct answer: a² − 2ab + b²

The correct answer is B: a² − 2ab + b². Begin with the full square area a². Removing the first strip subtracts ab, and removing the second strip subtracts another ab, giving a² − 2ab. However, the corner of area b² belongs to both removed strips, so it has been subtracted twice. To correct double subtraction, add b² back once. The result is a² − 2ab + b², which is also (a − b)². Option A subtracts the overlap one time too many. Option C adds the strip areas instead of removing them. Option D removes only the difference of two squares and does not represent this two-strip counting process. The key rule is: when an overlapping region is removed twice, add it back once.

Related tags

Square Of DifferenceOverlap ModelArea SubtractionVisual Models Of IdentitiesExploring Algebraic IdentitiesMathematicsClass 9 Mcq

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