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Subjects
Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesExpertLevel 64
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Which of the following factorisation identities is correct for all real values?

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Answer and explanation

Correct answer: \(a^3-b^3=(a-b)(a^2+ab+b^2)\)

The difference-of-cubes identity is \(a^3-b^3=(a-b)(a^2+ab+b^2)\). On multiplying, the middle terms \(-a^2b\) and \(+a^2b\) cancel. Exam tip: a difference of cubes always begins with \(a-b\).

Related tags

Algebraic IdentitiesDifference Of CubesFactorisationClass 9 MathematicsPolynomial Identities

Frequently asked questions

What is the correct answer to this question?

\(a^3-b^3=(a-b)(a^2+ab+b^2)\)

Why is this the correct answer?

The difference-of-cubes identity is \(a^3-b^3=(a-b)(a^2+ab+b^2)\). On multiplying, the middle terms \(-a^2b\) and \(+a^2b\) cancel. Exam tip: a difference of cubes always begins with \(a-b\).

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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