Which form is most suitable for finding (998^2) using an identity?
Answer and explanation
Correct answer: ( (1000-2)^2 )
The number 998 is very close to the convenient base 1000. It can be written as \\(998=1000-2\\), so its square can be found quickly with the identity \\((x-y)^2=x^2-2xy+y^2\\). Substituting \\(x=1000\\) and \\(y=2\\) gives \\(998^2=(1000-2)^2=1000000-4000+4=996004\\). This avoids long multiplication and uses a nearby round number.
Therefore, option B is the most suitable form. Option A, \\((998+2)^2\\), changes the number to 1000 and is not equal to \\(998^2\\). Option C represents 1002 rather than 998, and option D is the difference-of-squares product, not the square of 998. The key is to choose a close base and preserve the subtraction correctly.
Frequently asked questions
What is the correct answer to this question?
( (1000-2)^2 )
Why is this the correct answer?
The number 998 is very close to the convenient base 1000. It can be written as \\(998=1000-2\\), so its square can be found quickly with the identity \\((x-y)^2=x^2-2xy+y^2\\). Substituting \\(x=1000\\) and \\(y=2\\) gives \\(998^2=(1000-2)^2=1000000-4000+4=996004\\). This avoids long multiplication and uses a nearby round number.
Therefore, option B is the most suitable form. Option A, \\((998+2)^2\\), changes the number to 1000 and is not equal to \\(998^2\\). Option C represents 1002 rather than 998, and option D is the difference-of-squares product, not the square of 998. The key is to choose a close base and preserve the subtraction correctly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
