Using an algebraic identity, find the value of \(53\cdot47\).
Answer and explanation
Correct answer: 2491
\(53\cdot47=(50+3)(50-3)\). Using the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\), we get \(50^2-3^2=2500-9=2491\). Therefore, option A is correct. Option B, 2509, may result from adding 9 instead of subtracting it. Exam tip: When two numbers are equally above and below a common number, use the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
2491
Why is this the correct answer?
\(53\cdot47=(50+3)(50-3)\). Using the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\), we get \(50^2-3^2=2500-9=2491\). Therefore, option A is correct. Option B, 2509, may result from adding 9 instead of subtracting it. Exam tip: When two numbers are equally above and below a common 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
