Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Use the Binomial Theorem for fast numerical computation
Problem
Use the Binomial Theorem to evaluate \(101^3\).
Big Picture
What this problem is really about
Rewrite the number as an easy power-of-ten benchmark plus a small adjustment. The cube pattern then separates the computation into four manageable place-value contributions instead of one large multiplication. Keep both mixed terms, evaluate each contribution independently, and estimate the magnitude so a misplaced zero in the final sum is easy to catch.
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