What is the total (ab)-term in ( (a+b)^2+(b+c)^2+(c+a)^2 )?
Answer and explanation
Correct answer: \(2ab\)
Expanding \((a+b)^2\) gives \(a^2+2ab+b^2\), so its \(ab\)-term is \(2ab\). The mixed terms in \((b+c)^2\) and \((c+a)^2\) are \(2bc\) and \(2ca\), respectively, not \(ab\). Therefore, the total \(ab\)-term is \(2ab\). Exam tip: Expand each square separately and collect only the requested term.
Frequently asked questions
What is the correct answer to this question?
\(2ab\)
Why is this the correct answer?
Expanding \((a+b)^2\) gives \(a^2+2ab+b^2\), so its \(ab\)-term is \(2ab\). The mixed terms in \((b+c)^2\) and \((c+a)^2\) are \(2bc\) and \(2ca\), respectively, not \(ab\). Therefore, the total \(ab\)-term is \(2ab\). Exam tip: Expand each square separately and collect only the requested term.
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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