Which of the following expressions is a perfect-square trinomial and can therefore be factorised as the square of a binomial?
Answer and explanation
Correct answer: \(9p^2-12pq+4q^2\)
A perfect-square trinomial has the form \(a^2-2ab+b^2=(a-b)^2\). Here, \(9p^2=(3p)^2\), \(4q^2=(2q)^2\), and \(-12pq=-2(3p)(2q)\). Therefore, \(9p^2-12pq+4q^2=(3p-2q)^2\). In option B, the last term is \(2q^2\), not \(4q^2\), so it is not a perfect square. Exam tip: take the square roots of the first and last terms, then check whether the middle term is \(\pm2ab\).
Frequently asked questions
What is the correct answer to this question?
\(9p^2-12pq+4q^2\)
Why is this the correct answer?
A perfect-square trinomial has the form \(a^2-2ab+b^2=(a-b)^2\). Here, \(9p^2=(3p)^2\), \(4q^2=(2q)^2\), and \(-12pq=-2(3p)(2q)\). Therefore, \(9p^2-12pq+4q^2=(3p-2q)^2\). In option B, the last term is \(2q^2\), not \(4q^2\), so it is not a perfect square. Exam tip: take the square roots of the first and last terms, then check whether the middle term is \(\pm2ab\).
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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