Which of the following expressions is a difference of two squares, to which the identity \((a+b)(a-b)=a^2-b^2\) applies?
Answer and explanation
Correct answer: \(x^2-9\)
\(x^2-9=x^2-3^2\), so it has the form \(a^2-b^2\). Therefore, it factorises as \((x+3)(x-3)\). \(x^2+6x+9=(x+3)^2\) is a perfect-square trinomial, while \(x^2+9\) has a plus sign between the terms. Exam tip: look for two square terms separated by a minus sign before applying the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\(x^2-9\)
Why is this the correct answer?
\(x^2-9=x^2-3^2\), so it has the form \(a^2-b^2\). Therefore, it factorises as \((x+3)(x-3)\). \(x^2+6x+9=(x+3)^2\) is a perfect-square trinomial, while \(x^2+9\) has a plus sign between the terms. Exam tip: look for two square terms separated by a minus sign before applying the difference-of-squares identity.
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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