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If a visual model shows p²+q² with only one pq rectangle, what is missing to complete (p+q)²?

Answer and explanation

Correct answer: One more pq rectangle

Direct answer: Option A, one more pq rectangle, is correct. A square whose side is p+q can be divided into four regions: a p² square, a q² square, and two rectangles, each with area pq. Therefore (p+q)²=p²+pq+pq+q²=p²+2pq+q². The model already contains p², q² and one pq region, so exactly one further pq region is needed. Option B is wrong because p² is already present. Option C is wrong because q² is also already present. Option D describes a length, not an area region, and cannot supply the missing term. Memory cue: the middle term 2pq means two separate pq rectangles in the area model.

Related tags

Perfect SquareMissing RegionVisual IdentityArea TilesVisual Models Of IdentitiesExploring Algebraic IdentitiesMathematicsClass 9 Mcq

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