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What is the main visual difference between \((a+b)^2\) and \((a-b)^2\) in square models?

Answer and explanation

Correct answer: In the first parts are added and in the second some parts are subtracted

The correct answer is A. In the square model for \((a+b)^2\), the side is formed by joining lengths \(a\) and \(b\). The complete square can be divided into one \(a^2\) square, two \(ab\) rectangles, and one \(b^2\) square, so the parts are added: \(a^2+2ab+b^2\). In the model for \((a-b)^2\), a length \(b\) is removed from a length \(a\), so some strips or regions are subtracted, producing \(a^2-2ab+b^2\). Option B is false because both models represent positive areas when the side lengths are valid. Option C is false because both are area models, not just lines. Option D reverses the signs: \((a-b)^2\) has side \(a-b\), not always \(a+b\). The sign inside the bracket is the key visual clue.

Related tags

Plus Minus ModelsVisual DifferenceAlgebraic IdentitiesArea ModelBinomial SquaresVisual Models Of IdentitiesExploring Algebraic IdentitiesMathematics

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