Binomial Expansion of $$(a+b)^n+(a-b)^n$$

Binomial Expansion of $$(a+b)^n+(a-b)^n$$

## Formula

If $$n$$ is even:

$$(a+b)^n+(a-b)^n=2\sum_{\substack{r=0\\r\text{ even}}}^{n}{}^nC_ra^{n-r}b^r$$

If $$n$$ is odd, the same expression contains only even powers of $$b$$ up to $n-1$.

## Usage

- Used to isolate even powers in binomial expansions.