Which identity can quickly calculate \( 104\times96 \)?
Answer and explanation
Correct answer: \( (a+b)(a-b)=a^2-b^2 \)
Here, \(104=100+4\) and \(96=100-4\). Thus the product is of the form \((100+4)(100-4)\), so \((a+b)(a-b)=a^2-b^2\) applies. Hence, \(104\times96=100^2-4^2=10000-16=9984\). The identity \((a-b)^2\) is used for squaring one binomial, not for multiplying conjugate binomials. Exam tip: when two numbers are equally distant from the same number, look for the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\( (a+b)(a-b)=a^2-b^2 \)
Why is this the correct answer?
Here, \(104=100+4\) and \(96=100-4\). Thus the product is of the form \((100+4)(100-4)\), so \((a+b)(a-b)=a^2-b^2\) applies. Hence, \(104\times96=100^2-4^2=10000-16=9984\). The identity \((a-b)^2\) is used for squaring one binomial, not for multiplying conjugate binomials. Exam tip: when two numbers are equally distant from the same number, look for the difference-of-squares identity.
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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