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In an area model representing the square of \(a-b\), which type of region is subtracted twice?

Answer and explanation

Correct answer: A rectangular strip of area \(ab\)

The correct answer is B: an individual rectangular strip of area \(ab\) is subtracted twice. Start with the large square of area \(a^2\). To obtain a square of side \(a-b\), remove one horizontal strip of area \(ab\) and one vertical strip of area \(ab\). Thus the subtraction contains \(-ab-ab=-2ab\). The two strips overlap in a corner square of area \(b^2\), so that overlap is counted in both removals and must be added back once. Option A is the starting area, not a removed strip. C is the overlap that is restored, not the type of strip subtracted twice. D is not an area at all and does not describe the construction. Memory cue: the coefficient 2 in \(-2ab\) counts the two removed strips.

Related tags

Square Of DifferenceArea ModelRectangular StripsOverlapping RegionsVisual Models Of IdentitiesExploring Algebraic IdentitiesMathematicsClass 9 Mcq

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