What is the simplified form of ( (4a+b)^2-(4a-b)^2 )?
Answer and explanation
Correct answer: \(16ab\)
Apply the identity \((x+y)^2-(x-y)^2=4xy\). Here, \(x=4a\) and \(y=b\), so the expression becomes \(4\times4a\times b=16ab\). \(32ab\) results from introducing an extra factor of 2, so it is incorrect. Exam tip: Recognise this difference-of-squares identity before expanding the brackets.
Frequently asked questions
What is the correct answer to this question?
\(16ab\)
Why is this the correct answer?
Apply the identity \((x+y)^2-(x-y)^2=4xy\). Here, \(x=4a\) and \(y=b\), so the expression becomes \(4\times4a\times b=16ab\). \(32ab\) results from introducing an extra factor of 2, so it is incorrect. Exam tip: Recognise this difference-of-squares identity before expanding the brackets.
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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