What is the value of ( 1004^2-996^2 )?
Answer and explanation
Correct answer: (16000)
The expression has the form \(a^2-b^2\), so the difference-of-squares identity is the quickest method: \\(a^2-b^2=(a+b)(a-b)\\). Take \(a=1004\) and \(b=996\). Their sum is 2000, and their difference is 8. Therefore the required value is \\(2000\times8=16000\\).
Hence option A is correct. Calculating both large squares separately is unnecessary and creates more opportunity for arithmetic mistakes. The value 8000 would result from losing a factor of 2, while 4000 and 12000 do not match the product of the sum and difference. The identity works because the middle terms cancel when the two squares are subtracted.
Frequently asked questions
What is the correct answer to this question?
(16000)
Why is this the correct answer?
The expression has the form \(a^2-b^2\), so the difference-of-squares identity is the quickest method: \\(a^2-b^2=(a+b)(a-b)\\). Take \(a=1004\) and \(b=996\). Their sum is 2000, and their difference is 8. Therefore the required value is \\(2000\times8=16000\\).
Hence option A is correct. Calculating both large squares separately is unnecessary and creates more opportunity for arithmetic mistakes. The value 8000 would result from losing a factor of 2, while 4000 and 12000 do not match the product of the sum and difference. The identity works because the middle terms cancel when the two squares are subtracted.
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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