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Class 9MathematicsExploring Algebraic IdentitiesAlgebraic identitiesHardLevel 65
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If (x+y=13) and (xy=40), what is the value of (x^2+y^2)?

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Answer and explanation

Correct answer: 89

Using the identity \((x+y)^2=x^2+y^2+2xy\), we get \(x^2+y^2=(x+y)^2-2xy\). Therefore, \(x^2+y^2=13^2-2(40)=169-80=89\). Option 169 is only \((x+y)^2\); subtracting \(2xy\) is necessary. Exam tip: when the sum and product are given, start with \((x+y)^2-2xy\).

Related tags

Algebraic IdentitiesSum And ProductSquare Of SumQuadratic ExpressionsClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

89

Why is this the correct answer?

Using the identity \((x+y)^2=x^2+y^2+2xy\), we get \(x^2+y^2=(x+y)^2-2xy\). Therefore, \(x^2+y^2=13^2-2(40)=169-80=89\). Option 169 is only \((x+y)^2\); subtracting \(2xy\) is necessary. Exam tip: when the sum and product are given, start with \((x+y)^2-2xy\).

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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