Binomial expansion for any power

The idea

For negative and fractional $n$, when $|x| < 1$:$$(1 + x)^n = 1 + nx + \frac{n(n - 1)}{2!}x^2 + \frac{n(n - 1)(n - 2)}{3!}x^3 + \dots$$For $(a + bx)^n$, take out $a^n$ first.

1. Write it as $a^n\left(1 + \frac{b}{a}x\right)^n$.
2. Expand with $\frac{b}{a}x$ in place of $x$, keeping the brackets.
3. State the validity: $\left|\frac{b}{a}x\right| < 1$.

Watch out Factor out $a^n$, not $a$, from $(a + bx)^n$.