Find \( 72\times68 \) using an identity.
Answer and explanation
Correct answer: 4896
Write \(72\times68\) as \((70+2)(70-2)\). Using \((a+b)(a-b)=a^2-b^2\), we get \(70^2-2^2=4900-4=4896\). Hence, 4896 is correct. 4900 is only \(70^2\); subtracting \(2^2\) is necessary. Exam tip: use the difference-of-squares identity when two numbers are equally distant from a common number.
Frequently asked questions
What is the correct answer to this question?
4896
Why is this the correct answer?
Write \(72\times68\) as \((70+2)(70-2)\). Using \((a+b)(a-b)=a^2-b^2\), we get \(70^2-2^2=4900-4=4896\). Hence, 4896 is correct. 4900 is only \(70^2\); subtracting \(2^2\) is necessary. Exam tip: use the difference-of-squares identity when two numbers are equally distant from a common 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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