2.5 Algebraic Identities

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Solved Examples

Step 1

Write 999 as 1000−11000 - 1.

Step 2

Use (a−b)3=a3−b3−3ab(a−b)(a-b)^3 = a^3 - b^3 - 3ab(a-b).

Step 3

(1000−1)3=10003−13−3(1000)(1)(1000−1)(1000 - 1)^3 = 1000^3 - 1^3 - 3(1000)(1)(1000 - 1).

Step 4

=1000000000−1−3000(999)= 1000000000 - 1 - 3000(999).

Step 5

=1000000000−1−2997000=997002999= 1000000000 - 1 - 2997000 = 997002999.

Final Answer

997002999

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