n² + n = (n+1)² - (n+1)

This algebraic identity is useful for calculating expressions of the form $n^2+n$, especially when $n$ is close to a multiple of 10 or 5. By rewriting the expression, you can often simplify the squaring and subtraction involved.

For example, $89^2 + 89 = 90^2 - 90 = 8100 - 90 = 8010$.

The trick can also be applied in reverse: $66^2 - 66 = 65^2 + 65 = 4225 + 65 = 4290$.