Which is the factorisation of (25x^2-1)?
Answer and explanation
Correct answer: \((5x-1)(5x+1)\)
This expression is a difference of squares: \(25x^2-1=(5x)^2-1^2\). Applying \(a^2-b^2=(a-b)(a+b)\) gives \((5x-1)(5x+1)\). Options A and D are perfect squares; on expansion, they contain middle terms \(-10x\) and \(+10x\), respectively, which are not present in the expression. Exam tip: before factorising, check whether both terms are perfect squares separated by subtraction.
Frequently asked questions
What is the correct answer to this question?
\((5x-1)(5x+1)\)
Why is this the correct answer?
This expression is a difference of squares: \(25x^2-1=(5x)^2-1^2\). Applying \(a^2-b^2=(a-b)(a+b)\) gives \((5x-1)(5x+1)\). Options A and D are perfect squares; on expansion, they contain middle terms \(-10x\) and \(+10x\), respectively, which are not present in the expression. Exam tip: before factorising, check whether both terms are perfect squares separated by subtraction.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Quadratic expressions.
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