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Subjects
Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesExpertLevel 63
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What is the value of ( 998^2 ) using ( (1000-2)^2 )?

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Answer and explanation

Correct answer: 996004

Write 998 as \(1000-2\). Using \((a-b)^2=a^2-2ab+b^2\), we get \((1000-2)^2=1000^2-2\times1000\times2+2^2=1000000-4000+4=996004\). Therefore, option A is correct. Option D misses the final \(+4\) term. Exam tip: the middle term in \((a-b)^2\) is always negative.

Related tags

Algebraic IdentitiesSquare Of BinomialDifference Of SquaresMental ArithmeticClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

996004

Why is this the correct answer?

Write 998 as \(1000-2\). Using \((a-b)^2=a^2-2ab+b^2\), we get \((1000-2)^2=1000^2-2\times1000\times2+2^2=1000000-4000+4=996004\). Therefore, option A is correct. Option D misses the final \(+4\) term. Exam tip: the middle term in \((a-b)^2\) is always negative.

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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