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Which of the following trinomials can be written as the square of a binomial for all \(p\) and \(q\)?
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Answer and explanation
Correct answer: \(4p^2-12pq+9q^2\)
The end terms have roots \(2p\) and \(-3q\); twice their product is \(-12pq\). Therefore, A is \((2p-3q)^2\). C fails the middle-term test. Exam tip: always verify the middle coefficient.
Frequently asked questions
What is the correct answer to this question?
\(4p^2-12pq+9q^2\)
Why is this the correct answer?
The end terms have roots \(2p\) and \(-3q\); twice their product is \(-12pq\). Therefore, A is \((2p-3q)^2\). C fails the middle-term test. Exam tip: always verify the middle coefficient.
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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