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Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesExpertLevel 62
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What is the simplified form of ( (4x-5)^2-(16x^2+25) )?

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Answer and explanation

Correct answer: -40x

Using the identity a^2-2ab+b^2, (4x-5)^2=16x^2-40x+25. On subtracting (16x^2+25), both 16x^2 and 25 cancel, leaving -40x. Option D, -20x, may result from incorrectly taking half of the middle term 2(4x)(5)=40x. In exams, always check the sign and factor 2 in the middle term while expanding a square.

Related tags

Algebraic IdentitiesBinomial SquareExpression SimplificationPolynomial ExpansionClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

-40x

Why is this the correct answer?

Using the identity a^2-2ab+b^2, (4x-5)^2=16x^2-40x+25. On subtracting (16x^2+25), both 16x^2 and 25 cancel, leaving -40x. Option D, -20x, may result from incorrectly taking half of the middle term 2(4x)(5)=40x. In exams, always check the sign and factor 2 in the middle term while expanding a square.

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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