What is the value of ( (a+b)^2+(a-b)^2-2a^2-2b^2 )?
Answer and explanation
Correct answer: \(0\)
Use the identities \((a+b)^2=a^2+2ab+b^2\) and \((a-b)^2=a^2-2ab+b^2\). Their sum is \(2a^2+2b^2\), since the \(+2ab\) and \(-2ab\) terms cancel. Subtracting \(2a^2+2b^2\) therefore gives \(0\). \(2ab\) is not correct because the middle terms add to zero. Exam tip: remember \((x+y)^2+(x-y)^2=2x^2+2y^2\).
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
Use the identities \((a+b)^2=a^2+2ab+b^2\) and \((a-b)^2=a^2-2ab+b^2\). Their sum is \(2a^2+2b^2\), since the \(+2ab\) and \(-2ab\) terms cancel. Subtracting \(2a^2+2b^2\) therefore gives \(0\). \(2ab\) is not correct because the middle terms add to zero. Exam tip: remember \((x+y)^2+(x-y)^2=2x^2+2y^2\).
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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