Which of the following expressions can be factorised using the identity for the difference of two perfect squares?
Answer and explanation
Correct answer: \(81p^2-25q^2\)
\(81p^2-25q^2=(9p)^2-(5q)^2\). Therefore, using \(a^2-b^2=(a-b)(a+b)\), it factorises as \((9p-5q)(9p+5q)\). Option C is \((9p-5q)^2\), a perfect-square trinomial rather than a difference of two squares. Exam tip: a difference of squares has two square terms separated by a minus sign.
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What is the correct answer to this question?
\(81p^2-25q^2\)
Why is this the correct answer?
\(81p^2-25q^2=(9p)^2-(5q)^2\). Therefore, using \(a^2-b^2=(a-b)(a+b)\), it factorises as \((9p-5q)(9p+5q)\). Option C is \((9p-5q)^2\), a perfect-square trinomial rather than a difference of two squares. Exam tip: a difference of squares has two square terms separated by a minus sign.
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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