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Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesMedium
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What is the simplified form of ( (3x-1)^2-(9x^2+1) )?

Answer and explanation

Correct answer: -6x

Using the identity

(a-b)^2=a^2-2ab+b^2,

with a=3x and b=1, we get (3x-1)^2=9x^2-6x+1. Therefore,

9x^2-6x+1-(9x^2+1)=-6x.

Hence, -6x is the correct answer. The option 6x results from missing the negative sign of the middle term. Exam tip: in (a-b)^2, the middle term is always -2ab.

Related tags

Algebraic IdentitiesBinomial SquarePolynomial SimplificationGrade 9 MathematicsExploring Algebraic IdentitiesMathematicsClass 9 Mcq
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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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