To calculate \( 63\times57 \) quickly, which form is correct?
Answer and explanation
Correct answer: \( (60+3)(60-3) \)
Since \(63=60+3\) and \(57=60-3\), we can write \(63\times57=(60+3)(60-3)\). Using \((a+b)(a-b)=a^2-b^2\), the value is \(60^2-3^2=3600-9=3591\). Option A represents \(63\times63\), while option B represents \(57\times57\). Exam tip: use the difference-of-squares identity when two factors are equally spaced from the same middle number.
Frequently asked questions
What is the correct answer to this question?
\( (60+3)(60-3) \)
Why is this the correct answer?
Since \(63=60+3\) and \(57=60-3\), we can write \(63\times57=(60+3)(60-3)\). Using \((a+b)(a-b)=a^2-b^2\), the value is \(60^2-3^2=3600-9=3591\). Option A represents \(63\times63\), while option B represents \(57\times57\). Exam tip: use the difference-of-squares identity when two factors are equally spaced from the same middle number.
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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