What is the simplified form of ( (x+4)^2-(x-4)^2 )?
Answer and explanation
Correct answer: \(16x\)
Use the identity \((a+b)^2-(a-b)^2=4ab\). Here, \(a=x\) and \(b=4\), so the expression becomes \(4\times x\times 4=16x\). The result \(8x\) would arise if \(b=2\). Exam tip: Recognise the difference-of-squares identity to simplify such expressions quickly instead of expanding both squares.
Frequently asked questions
What is the correct answer to this question?
\(16x\)
Why is this the correct answer?
Use the identity \((a+b)^2-(a-b)^2=4ab\). Here, \(a=x\) and \(b=4\), so the expression becomes \(4\times x\times 4=16x\). The result \(8x\) would arise if \(b=2\). Exam tip: Recognise the difference-of-squares identity to simplify such expressions quickly instead of expanding both squares.
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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