What is the simplified form of ( (a+b)^3-(a^3+b^3) )?
Answer and explanation
Correct answer: \(3ab(a+b)\)
Use the identity \((a+b)^3=a^3+3a^2b+3ab^2+b^3\). After subtracting \(a^3+b^3\), the remaining expression is \(3a^2b+3ab^2\). Taking \(3ab\) as the common factor gives \(3ab(a+b)\). In \(3ab(a-b)\), the second middle term would be negative, so it is incorrect. Exam tip: while expanding a cube, check the signs of both middle terms carefully.
Frequently asked questions
What is the correct answer to this question?
\(3ab(a+b)\)
Why is this the correct answer?
Use the identity \((a+b)^3=a^3+3a^2b+3ab^2+b^3\). After subtracting \(a^3+b^3\), the remaining expression is \(3a^2b+3ab^2\). Taking \(3ab\) as the common factor gives \(3ab(a+b)\). In \(3ab(a-b)\), the second middle term would be negative, so it is incorrect. Exam tip: while expanding a cube, check the signs of both middle 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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