(x + y)ⁿ = Σ C(n, r) x^(n-r) y^r.

The sum of coefficients in any binomial expansion equals 2ⁿ.

The coefficient of x⁸ in (1 - x² + x⁴)^5 is $x$.

(1.01)⁵ approximated using binomial theorem is approximately:

The last digit of 7¹⁰⁰ is:

In the expansion of (x + y)^n, coefficients are symmetric: C(n, r) = C(n, n-r).