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Each side of a square model is divided into parts x and y. The model contains one square of area x², one square of area y², and two rectangles of area xy. Which algebraic identity does this model represent?
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Answer and explanation
Correct answer: \((x+y)^2=x^2+2xy+y^2\)
The whole square has side \(x+y\), so its area is \((x+y)^2\). Adding the four regions gives \(x^2+xy+xy+y^2=x^2+2xy+y^2\). Option A has a negative middle term. Exam tip: always count both \(xy\) rectangles.
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What is the correct answer to this question?
\((x+y)^2=x^2+2xy+y^2\)
Why is this the correct answer?
The whole square has side \(x+y\), so its area is \((x+y)^2\). Adding the four regions gives \(x^2+xy+xy+y^2=x^2+2xy+y^2\). Option A has a negative middle term. Exam tip: always count both \(xy\) rectangles.
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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