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What is the fastest way to calculate 982−2298^2 - 2^2?

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Full solution

Q. What is the fastest way to calculate 982−2298^2 - 2^2?
  1. Apply formula: We can use the difference of squares formula, which states that a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b), where aa and bb are any real numbers. Here, aa is 9898 and bb is 22.
  2. Use formula: Apply the difference of squares formula to 982−2298^2 - 2^2 to get (98+2)(98−2)(98 + 2)(98 - 2).
  3. Calculate sums and differences: Calculate the sums and differences inside the parentheses: 98+2=10098 + 2 = 100 and 98−2=9698 - 2 = 96.
  4. Multiply results: Multiply the results from the previous step: 100×96100 \times 96.
  5. Perform final multiplication: Perform the multiplication to find the final answer: 100×96=9600100 \times 96 = 9600.

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