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What is the simplified form of ( (x+y)^2-(x-y)^2+ (x+2y)^2-(x-2y)^2 )?
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Answer and explanation
Correct answer: \(12xy\)
For the first part, \((x+y)^2-(x-y)^2=4xy\). Similarly, \((x+2y)^2-(x-2y)^2=8xy\). Therefore, the total is \(4xy+8xy=12xy\). It is not \(16xy\), because the two differences add up to 12. Exam tip: apply the identity \((a+b)^2-(a-b)^2=4ab\) directly.
Frequently asked questions
What is the correct answer to this question?
\(12xy\)
Why is this the correct answer?
For the first part, \((x+y)^2-(x-y)^2=4xy\). Similarly, \((x+2y)^2-(x-2y)^2=8xy\). Therefore, the total is \(4xy+8xy=12xy\). It is not \(16xy\), because the two differences add up to 12. Exam tip: apply the identity \((a+b)^2-(a-b)^2=4ab\) directly.
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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