Simplify ( (a+b)^2-(a^2+b^2) ).
Answer and explanation
Correct answer: \(2ab\)
Using the identity \((a+b)^2=a^2+2ab+b^2\), the expression becomes \(a^2+2ab+b^2-(a^2+b^2)\). The terms \(a^2\) and \(b^2\) cancel, leaving \(2ab\). It is not \(0\) because the middle term \(2ab\) does not cancel. Exam tip: expand the identity first, then cancel like terms carefully.
Frequently asked questions
What is the correct answer to this question?
\(2ab\)
Why is this the correct answer?
Using the identity \((a+b)^2=a^2+2ab+b^2\), the expression becomes \(a^2+2ab+b^2-(a^2+b^2)\). The terms \(a^2\) and \(b^2\) cancel, leaving \(2ab\). It is not \(0\) because the middle term \(2ab\) does not cancel. Exam tip: expand the identity first, then cancel 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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