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Observe the following pattern. 2³ - 1³ = 1 + 2 × 1 × 3 3³-2³=1+3× 2 × 3 4³-3³= 1+ 4×3×3 Using the pattern, find the value of each of the following. 81³-80³ ​

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Answer:

To find the value of 81³ - 80³ using the given pattern, we can follow the same approach as in the previous examples.

1. Start by expressing the difference of cubes, 81³ - 80³, as a sum.

81³ - 80³ = (1 + 2 × 1 × 3) + (1 + 3 × 2 × 3) + ...

2. Expand the terms based on the pattern.

81³ - 80³ = 1 + 2 × 1 × 3 + 1 + 3 × 2 × 3 + ...

3. Simplify each term.

81³ - 80³ = 1 + 6 + 1 + 18 + ...

4. Continue this pattern until you reach the desired term.

81³ - 80³ = 1 + 6 + 1 + 18 + ...

5. Add up the simplified terms.

81³ - 80³ = 26 + ...

Therefore, the value of 81³ - 80³ is 26.

By following the given pattern, we can find the value of the expression by expanding it into a sum of terms and simplifying each term according to the pattern. In this case, the pattern involves the difference of cubes and the multiplication of certain numbers.

Explanation:

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