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Which of the following expressions is a perfect-square trinomial and can be factorised using the identity \((a-b)^2\)?
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Answer and explanation
Correct answer: \(49p^2-70pq+25q^2\)
In \((a-b)^2=a^2-2ab+b^2\), the middle term is negative. Here, \(2\times7p\times5q=70pq\), so option A is \((7p-5q)^2\). Option D has a positive middle term and matches \((a+b)^2\). Exam tip: always check the sign of the middle term.
Frequently asked questions
What is the correct answer to this question?
\(49p^2-70pq+25q^2\)
Why is this the correct answer?
In \((a-b)^2=a^2-2ab+b^2\), the middle term is negative. Here, \(2\times7p\times5q=70pq\), so option A is \((7p-5q)^2\). Option D has a positive middle term and matches \((a+b)^2\). Exam tip: always 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: Factorisation.
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