Choose the factorised form of \(4m^2+4mn+n^2\).
Answer and explanation
Correct answer: \((2m+n)^2\)
Use the identity \(a^2+2ab+b^2=(a+b)^2\) with \(a=2m\) and \(b=n\). Then \(a^2=4m^2\), \(2ab=4mn\), and \(b^2=n^2\). Hence, \(4m^2+4mn+n^2=(2m+n)^2\). The close distractor \((2m-n)^2\) expands to give a middle term of \(-4mn\), so it is incorrect. Exam tip: for a perfect square, check both the sign and coefficient of the middle term.
Frequently asked questions
What is the correct answer to this question?
\((2m+n)^2\)
Why is this the correct answer?
Use the identity \(a^2+2ab+b^2=(a+b)^2\) with \(a=2m\) and \(b=n\). Then \(a^2=4m^2\), \(2ab=4mn\), and \(b^2=n^2\). Hence, \(4m^2+4mn+n^2=(2m+n)^2\). The close distractor \((2m-n)^2\) expands to give a middle term of \(-4mn\), so it is incorrect. Exam tip: for a perfect square, check both the sign and coefficient of the middle term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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