Which of the following trinomials can be factorised directly using a perfect-square identity?
Answer and explanation
Correct answer: \(9p^2-12pq+4q^2\)
Here \(9p^2=(3p)^2\) and \(4q^2=(2q)^2\). The middle term is \(-12pq=-2(3p)(2q)\), so it matches \((3p-2q)^2\). Option C also forms a square, but it has a positive middle term. Exam tip: take square roots of the end terms, then check the sign of the middle term.
Frequently asked questions
What is the correct answer to this question?
\(9p^2-12pq+4q^2\)
Why is this the correct answer?
Here \(9p^2=(3p)^2\) and \(4q^2=(2q)^2\). The middle term is \(-12pq=-2(3p)(2q)\), so it matches \((3p-2q)^2\). Option C also forms a square, but it has a positive middle term. Exam tip: take square roots of the end terms, then check the sign of 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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