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Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesHardLevel 64
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For two algebraic expressions \(U\) and \(V\), which part remains unchanged in the expansions of \((U+V)^2\) and \((U-V)^2\)?

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Answer and explanation

Correct answer: \(U^2+V^2\)

Since \((U+V)^2=U^2+2UV+V^2\) and \((U-V)^2=U^2-2UV+V^2\), \(U^2+V^2\) remains unchanged. Only the middle term changes sign. Exam tip: compare the outer terms first.

Related tags

Algebraic IdentitiesSquare Of BinomialSign ChangeAlgebraic ExpressionsClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

\(U^2+V^2\)

Why is this the correct answer?

Since \((U+V)^2=U^2+2UV+V^2\) and \((U-V)^2=U^2-2UV+V^2\), \(U^2+V^2\) remains unchanged. Only the middle term changes sign. Exam tip: compare the outer terms first.

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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