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Using the identity \((a-b)^2=a^2-2ab+b^2\), what is the value of \(99^2\)?
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Answer and explanation
Correct answer: 9801
Since \(99=100-1\), \(99^2=(100-1)^2=100^2-2\times100\times1+1^2=10000-200+1=9801\). Option B does not correctly account for subtracting 200. In exams, express a number near 100 as \((a-b)\) to calculate its square quickly.
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What is the correct answer to this question?
9801
Why is this the correct answer?
Since \(99=100-1\), \(99^2=(100-1)^2=100^2-2\times100\times1+1^2=10000-200+1=9801\). Option B does not correctly account for subtracting 200. In exams, express a number near 100 as \((a-b)\) to calculate its square quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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