What is the value of ( 51^2-49^2 )?
Answer and explanation
Correct answer: 200
Use the identity \(a^2-b^2=(a+b)(a-b)\). Here, \(51^2-49^2=(51+49)(51-49)=100\times2=200\). Option 100 is only the sum of the two numbers, while 2 is their difference; their product gives the required value. Exam tip: for the difference of squares of nearby numbers, apply this identity directly.
Frequently asked questions
What is the correct answer to this question?
200
Why is this the correct answer?
Use the identity \(a^2-b^2=(a+b)(a-b)\). Here, \(51^2-49^2=(51+49)(51-49)=100\times2=200\). Option 100 is only the sum of the two numbers, while 2 is their difference; their product gives the required value. Exam tip: for the difference of squares of nearby numbers, apply this identity directly.
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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