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Simplification & Approximation · Question 46 of 71

Question 46

MediumOriginal question

Using an identity, find 998×1002998 \times 1002.

Options for question 46

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Write it as (1000−2)(1000+2)(1000 - 2)(1000 + 2).

  2. (a−b)(a+b)=a2−b2(a - b)(a + b) = a^2 - b^2, so the product is 1000000−4=9999961000000 - 4 = 999996.

Worth noting

The answer must be a little less than one million, because b2b^2 is subtracted. Adding 4 gives 1,000,004.

Concept
Using (a − b)(a + b) = a² − b² for quick products
Typical time
45 s
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