Factorise \(4y^2+4y+1\).
Answer and explanation
Correct answer: \((2y+1)^2\)
This is a perfect-square trinomial. We have \(4y^2=(2y)^2\), \(1=1^2\), and the middle term is \(2\times 2y\times 1=4y\). Hence, \(4y^2+4y+1=(2y+1)^2\). The closest distractor, \((2y-1)^2\), expands to \(4y^2-4y+1\), which has a negative middle term. Exam tip: check the sign of the middle term in \(a^2+2ab+b^2=(a+b)^2\).
Frequently asked questions
What is the correct answer to this question?
\((2y+1)^2\)
Why is this the correct answer?
This is a perfect-square trinomial. We have \(4y^2=(2y)^2\), \(1=1^2\), and the middle term is \(2\times 2y\times 1=4y\). Hence, \(4y^2+4y+1=(2y+1)^2\). The closest distractor, \((2y-1)^2\), expands to \(4y^2-4y+1\), which has a negative middle term. Exam tip: check the sign of the middle term in \(a^2+2ab+b^2=(a+b)^2\).
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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