Which of the following expressions can be factorised directly using the identity for the difference of squares?
Answer and explanation
Correct answer: \(x^2-49\)
\(x^2-49=x^2-7^2\), which matches \(a^2-b^2=(a-b)(a+b)\). Therefore, it factorises as \((x-7)(x+7)\). Option C is a perfect-square trinomial, \((x+7)^2\), not a difference of squares. Exam tip: check that both terms are perfect squares with a minus sign between them.
Frequently asked questions
What is the correct answer to this question?
\(x^2-49\)
Why is this the correct answer?
\(x^2-49=x^2-7^2\), which matches \(a^2-b^2=(a-b)(a+b)\). Therefore, it factorises as \((x-7)(x+7)\). Option C is a perfect-square trinomial, \((x+7)^2\), not a difference of squares. Exam tip: check that both terms are perfect squares with a minus sign between them.
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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