Binomial expansion

The idea

$$(a + b)^n = a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \dots + b^n$$The term in $b^r$ is $\binom{n}{r}a^{n-r}b^r$.

1. Write the general term $\binom{n}{r}a^{n-r}b^r$.
2. Choose $r$ to give the power of $x$ you want.
3. Raise the whole of $b$, coefficient and sign included, to the power $r$.

Watch out In $(1 + 2x)^6$, the $x^3$ term uses $(2x)^3 = 8x^3$, not $2x^3$.