What is the simplified form of ( (a+b)^2-(a^2-b^2) )?
Answer and explanation
Correct answer: \(2ab+2b^2\)
Using \((a+b)^2=a^2+2ab+b^2\), subtracting \(a^2-b^2\) changes the signs of both terms inside it. Thus, \(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Option B misses the remaining \(2b^2\) term. Exam tip: when a bracket is preceded by a minus sign, change the sign of every term in that bracket.
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What is the correct answer to this question?
\(2ab+2b^2\)
Why is this the correct answer?
Using \((a+b)^2=a^2+2ab+b^2\), subtracting \(a^2-b^2\) changes the signs of both terms inside it. Thus, \(a^2+2ab+b^2-a^2+b^2=2ab+2b^2\). Option B misses the remaining \(2b^2\) term. Exam tip: when a bracket is preceded by a minus sign, change the sign of every term in that bracket.
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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