Mathematics

You're computing a perfect square that's close to a round number—the key is to rewrite $401$ as $400 + 1$ and use the binomial expansion $(a+b)^2 = a^2 + 2ab + b^2$. This turns a tricky multiplication into three easy pieces: the square of the base, twice the cross term, and the square of the small adjustment. It's much faster than multiplying $401 \times 401$ directly.

You're computing a perfect square that's close to a round number—the key is to rewrite $401$ as $400 + 1$ and use the binomial expansion $(a+b)^2 = a^2 + 2ab + b^2$. This turns a tricky multiplication into three easy pieces: the square of the base, twice the cross term, and the square of the small adjustment. It's much faster than multiplying $401 \times 401$ directly.