Which of the following expressions can be identified and factorised as a difference of two squares?
Answer and explanation
Correct answer: \(p^2-q^2\)
\(p^2-q^2\) is a difference of two perfect squares. Applying \(a^2-b^2=(a-b)(a+b)\), it factorises as \((p-q)(p+q)\). In \(p^2+q^2\), the squares are added, not subtracted, so it does not fit this identity. Also, \(p^2\pm2pq+q^2\) are perfect-square trinomials: \((p+q)^2\) and \((p-q)^2\). Exam tip: when two square terms are separated by a minus sign, check for \((a-b)(a+b)\).
Frequently asked questions
What is the correct answer to this question?
\(p^2-q^2\)
Why is this the correct answer?
\(p^2-q^2\) is a difference of two perfect squares. Applying \(a^2-b^2=(a-b)(a+b)\), it factorises as \((p-q)(p+q)\). In \(p^2+q^2\), the squares are added, not subtracted, so it does not fit this identity. Also, \(p^2\pm2pq+q^2\) are perfect-square trinomials: \((p+q)^2\) and \((p-q)^2\). Exam tip: when two square terms are separated by a minus sign, check for \((a-b)(a+b)\).
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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