Which of the following expressions can be factorised using the identity of difference of squares, \(a^2-b^2=(a-b)(a+b)\)?
Answer and explanation
Correct answer: \(49a^2-b^2\)
\(49a^2-b^2=(7a)^2-b^2\), so it is the difference of two perfect squares. Applying \(a^2-b^2=(a-b)(a+b)\) gives \((7a-b)(7a+b)\). Option B is a sum of squares, while C and D are \((7a-b)^2\) and \((7a+b)^2\), respectively. Exam tip: for a difference of squares, check that there is a minus sign between the two square terms.
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What is the correct answer to this question?
\(49a^2-b^2\)
Why is this the correct answer?
\(49a^2-b^2=(7a)^2-b^2\), so it is the difference of two perfect squares. Applying \(a^2-b^2=(a-b)(a+b)\) gives \((7a-b)(7a+b)\). Option B is a sum of squares, while C and D are \((7a-b)^2\) and \((7a+b)^2\), respectively. Exam tip: for a difference of squares, check that there is a minus sign between the two square terms.
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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