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Subjects
Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesHardLevel 64
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Which of the following expressions is a perfect-square trinomial for every a and b?

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Answer and explanation

Correct answer: \(4a^2+12ab+9b^2\)

Here \(4a^2=(2a)^2\) and \(9b^2=(3b)^2\). The required middle term is \(2\times2a\times3b=12ab\), so the expression is \((2a+3b)^2\). Exam tip: always check both the sign and coefficient of the middle term.

Related tags

Algebraic IdentitiesPerfect Square TrinomialBinomial SquareGrade 9 MathematicsPolynomial Identification

Frequently asked questions

What is the correct answer to this question?

\(4a^2+12ab+9b^2\)

Why is this the correct answer?

Here \(4a^2=(2a)^2\) and \(9b^2=(3b)^2\). The required middle term is \(2\times2a\times3b=12ab\), so the expression is \((2a+3b)^2\). Exam tip: always check both the sign and coefficient of the middle term.

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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