Which is the correct factorisation of (a^2-b^2)?
Answer and explanation
Correct answer: \((a-b)(a+b)\)
\(a^2-b^2\) is a difference of two squares. Using \(x^2-y^2=(x-y)(x+y)\), with \(x=a\) and \(y=b\), gives \((a-b)(a+b)\). The expansion of \((a-b)^2\) is \(a^2-2ab+b^2\), so it is not correct. Exam tip: for a difference of squares, write the difference factor first and the sum factor next.
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What is the correct answer to this question?
\((a-b)(a+b)\)
Why is this the correct answer?
\(a^2-b^2\) is a difference of two squares. Using \(x^2-y^2=(x-y)(x+y)\), with \(x=a\) and \(y=b\), gives \((a-b)(a+b)\). The expansion of \((a-b)^2\) is \(a^2-2ab+b^2\), so it is not correct. Exam tip: for a difference of squares, write the difference factor first and the sum factor next.
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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