Evaluate
\[ (99)^3 \]
Solution:
Using identity:
\[ (a-b)^3 = a^3-b^3-3ab(a-b) \]
\[ (99)^3 = (100-1)^3 \]
\[ = (100)^3-(1)^3-3(100)(1)(100-1) \]
\[ = 1000000-1-300(99) \]
\[ = 1000000-1-29700 \]
\[ = 970299 \]
\[ (99)^3 \]
Using identity:
\[ (a-b)^3 = a^3-b^3-3ab(a-b) \]
\[ (99)^3 = (100-1)^3 \]
\[ = (100)^3-(1)^3-3(100)(1)(100-1) \]
\[ = 1000000-1-300(99) \]
\[ = 1000000-1-29700 \]
\[ = 970299 \]