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Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesExpertLevel 62
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Which of the following expressions can be factorised in the form of a difference of two squares, \(a^2-b^2\)?

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Answer and explanation

Correct answer: \(4p^2-25q^2\)

\(4p^2-25q^2=(2p)^2-(5q)^2\), so it is a difference of squares and factorises as \((2p-5q)(2p+5q)\). The other options are perfect-square trinomials. Exam tip: first check whether both terms are perfect squares with a minus sign.

Related tags

Algebraic IdentitiesDifference Of SquaresFactorisationPerfect Square TrinomialsClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

\(4p^2-25q^2\)

Why is this the correct answer?

\(4p^2-25q^2=(2p)^2-(5q)^2\), so it is a difference of squares and factorises as \((2p-5q)(2p+5q)\). The other options are perfect-square trinomials. Exam tip: first check whether both terms are perfect squares with a minus sign.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.

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10 more MCQs
  1. 1What is the correct expansion of the identity ( (a+b)^2 )?
  2. 2Choose the correct expansion of the identity ( (x-y)^2 ).
  3. 3The identity ( (p+q)(p-q) ) is equal to what?
  4. 4Which of the following identities represents the factorisation of the difference of two squares?
  5. 5Which of the following identities represents the square of the difference of two terms?
  6. 6In the expansion of which of the following identities is the middle term negative?
  7. 7Which of the following expressions can be written as a product of two binomials using the identity for the difference of squares?
  8. 8Which of the following expressions can be factorised using the identity \(a^2-b^2=(a-b)(a+b)\)?
  9. 9Which algebraic identity is used to factorise a difference of two squares?
  10. 10What is the middle term in ( (3a+2b)^2 )?
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