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Class 9MathematicsExploring Algebraic IdentitiesQuadratic expressionsMedium
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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.

Related tags

Algebraic IdentitiesDifference Of SquaresQuadratic ExpressionsFactorisationClass 9 MathematicsExploring Algebraic IdentitiesMathematicsClass 9 Mcq
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10 more MCQs
  1. 1Which expression can be factorised using the difference-of-cubes identity?
  2. 2What will be the factorised form of (r^2-2rs+s^2)?
  3. 3Which expression can be factorised directly using the identity for the difference of two squares?
  4. 4Which expression can be factorised directly using the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\)?
  5. 5Which expression is a quadratic expression?
  6. 6Based on the powers of the variable \(x\) in the polynomial \(5x^2-3x+7\), what is the degree of this expression?
  7. 7If a, b and c are constants, which condition is necessary for \(ax^2+bx+c\) to be a quadratic expression in x?
  8. 8If a quadratic expression has the general form \(ax^2+bx+c\), which condition on \(a\) is necessary for it to be quadratic?
  9. 9Which of the following expressions represents the square of the difference of two terms?
  10. 10Which of the following quadratic expressions can be factorised using the identity for the difference of two squares?
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