Which of the following expressions is a difference of two squares and can be factorised using the identity?
Answer and explanation
Correct answer: \(x^2-49\)
\(x^2-49=x^2-7^2\), so it is of the form \(a^2-b^2=(a-b)(a+b)\). Hence, its factorisation is \((x-7)(x+7)\). \(x^2+49\) is a sum of squares, whereas \(x^2+14x+49=(x+7)^2\) is a perfect-square trinomial. Exam tip: look for two perfect-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?
\(x^2-49\)
Why is this the correct answer?
\(x^2-49=x^2-7^2\), so it is of the form \(a^2-b^2=(a-b)(a+b)\). Hence, its factorisation is \((x-7)(x+7)\). \(x^2+49\) is a sum of squares, whereas \(x^2+14x+49=(x+7)^2\) is a perfect-square trinomial. Exam tip: look for two perfect-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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