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Riya wrote that \(x^2-49=(x-7)^2\). Which is the correct factorisation of \(x^2-49\) to correct her error?
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Answer and explanation
Correct answer: \((x-7)(x+7)\)
\(x^2-49=x^2-7^2\) is a difference of squares. Using \(a^2-b^2=(a-b)(a+b)\), it becomes \((x-7)(x+7)\). In contrast, \((x-7)^2\) contains the middle term \(-14x\). Exam tip: check for two squared terms with subtraction.
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What is the correct answer to this question?
\((x-7)(x+7)\)
Why is this the correct answer?
\(x^2-49=x^2-7^2\) is a difference of squares. Using \(a^2-b^2=(a-b)(a+b)\), it becomes \((x-7)(x+7)\). In contrast, \((x-7)^2\) contains the middle term \(-14x\). Exam tip: check for two squared terms with subtraction.
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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