Which is the correct expansion of ( (2x+1)^2 )?
Answer and explanation
Correct answer: \(4x^2+4x+1\)
Using the identity \((a+b)^2=a^2+2ab+b^2\), take \(a=2x\) and \(b=1\). Then \((2x+1)^2=(2x)^2+2(2x)(1)+1^2=4x^2+4x+1\). Hence, option D is correct. In option C, the middle term is written as \(2x\), but it should be \(4x\). Exam tip: calculate \(2ab\) separately to avoid errors in the middle term.
Frequently asked questions
What is the correct answer to this question?
\(4x^2+4x+1\)
Why is this the correct answer?
Using the identity \((a+b)^2=a^2+2ab+b^2\), take \(a=2x\) and \(b=1\). Then \((2x+1)^2=(2x)^2+2(2x)(1)+1^2=4x^2+4x+1\). Hence, option D is correct. In option C, the middle term is written as \(2x\), but it should be \(4x\). Exam tip: calculate \(2ab\) separately to avoid errors in the middle term.
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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