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If \(x>y\), which product represents the remaining area in a visual model after a square of side \(y\) is removed from a square of side \(x\)?
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Answer and explanation
Correct answer: \((x+y)(x-y)\)
The remaining area is \(x^2-y^2\). By the difference-of-squares identity, \(x^2-y^2=(x+y)(x-y)\), so A is correct. \((x-y)^2\) is the area of a smaller square, not the leftover region. Exam tip: a removed square usually signals difference of squares.
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What is the correct answer to this question?
\((x+y)(x-y)\)
Why is this the correct answer?
The remaining area is \(x^2-y^2\). By the difference-of-squares identity, \(x^2-y^2=(x+y)(x-y)\), so A is correct. \((x-y)^2\) is the area of a smaller square, not the leftover region. Exam tip: a removed square usually signals difference of squares.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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