Which of the following trinomials is a perfect-square expression?
Answer and explanation
Correct answer: \(9p^2-24pq+16q^2\)
We have \(9p^2=(3p)^2\) and \(16q^2=(4q)^2\). For a perfect-square trinomial, the middle term must be \(\pm2ab\). Here, \(2\times3p\times4q=24pq\), and the middle term is \(-24pq\). Therefore, \(9p^2-24pq+16q^2=(3p-4q)^2\), so option A is correct. In option B, the middle term is \(-20pq\), not the required \(-24pq\). Exam tip: take the square roots of the first and last terms, then check twice their product against the middle term.
Frequently asked questions
What is the correct answer to this question?
\(9p^2-24pq+16q^2\)
Why is this the correct answer?
We have \(9p^2=(3p)^2\) and \(16q^2=(4q)^2\). For a perfect-square trinomial, the middle term must be \(\pm2ab\). Here, \(2\times3p\times4q=24pq\), and the middle term is \(-24pq\). Therefore, \(9p^2-24pq+16q^2=(3p-4q)^2\), so option A is correct. In option B, the middle term is \(-20pq\), not the required \(-24pq\). Exam tip: take the square roots of the first and last terms, then check twice their product against 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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