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Using an algebraic identity, find the value of \(72\cdot68\).
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Answer and explanation
Correct answer: 4896
Here, \(72=70+2\) and \(68=70-2\). Therefore, \((70+2)(70-2)=70^2-2^2=4900-4=4896\). The identity used is \((a+b)(a-b)=a^2-b^2\). Exam tip: When two numbers are equally spaced around a central number, use the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
4896
Why is this the correct answer?
Here, \(72=70+2\) and \(68=70-2\). Therefore, \((70+2)(70-2)=70^2-2^2=4900-4=4896\). The identity used is \((a+b)(a-b)=a^2-b^2\). Exam tip: When two numbers are equally spaced around a central number, use the difference-of-squares identity.
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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