Which reason correctly identifies \(p^2-10pq+25q^2\) as a perfect-square trinomial?
Answer and explanation
Correct answer: The first and last terms are perfect squares, and the middle term is \(-2\) times the product of their square roots.
It matches \(a^2-2ab+b^2=(a-b)^2\), with \(a=p\) and \(b=5q\). Check the middle term: \(-2\times p\times5q=-10pq\). Perfect-square outer terms alone are not enough. In exams, always verify the \(\pm2ab\) term.
Frequently asked questions
What is the correct answer to this question?
The first and last terms are perfect squares, and the middle term is \(-2\) times the product of their square roots.
Why is this the correct answer?
It matches \(a^2-2ab+b^2=(a-b)^2\), with \(a=p\) and \(b=5q\). Check the middle term: \(-2\times p\times5q=-10pq\). Perfect-square outer terms alone are not enough. In exams, always verify the \(\pm2ab\) 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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