When is it true (x+y)^n=x^n + y^n ?? Any thoughts?
It's called Child's Binomial Theorem. If $\displaystyle n = 1$, it's true. If $\displaystyle n \ge 2$, not so much. For all $\displaystyle n\in\mathbb{N}$, though, $\displaystyle \displaystyle (x+y)^n = \sum_{k=0}^n {n \choose k}x^{n-k}y^k $ (call it Grown-up's Binomial Theorem).