What is the value of ( (x+y)^2+(x-y)^2-2x^2 )?
Answer and explanation
Correct answer: \(2y^2\)
On expanding, \((x+y)^2=x^2+2xy+y^2\) and \((x-y)^2=x^2-2xy+y^2\). When these are added, \(2xy\) and \(-2xy\) cancel, giving \(2x^2+2y^2\). Subtracting \(2x^2\) leaves \(2y^2\). Hence, \(2y^2\) is correct; \(2xy\) does not remain because the middle terms cancel. Exam tip: expand both squares first and combine like terms carefully.
Frequently asked questions
What is the correct answer to this question?
\(2y^2\)
Why is this the correct answer?
On expanding, \((x+y)^2=x^2+2xy+y^2\) and \((x-y)^2=x^2-2xy+y^2\). When these are added, \(2xy\) and \(-2xy\) cancel, giving \(2x^2+2y^2\). Subtracting \(2x^2\) leaves \(2y^2\). Hence, \(2y^2\) is correct; \(2xy\) does not remain because the middle terms cancel. Exam tip: expand both squares first and combine like terms carefully.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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