When is it true (x+y)^n=x^n + y^n ?? Any thoughts?

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- Sep 6th 2010, 02:42 PMzg12When is it true (x+y)^n=x^n + y^n ??
When is it true (x+y)^n=x^n + y^n ?? Any thoughts?

- Sep 6th 2010, 02:48 PMTheCoffeeMachine
It's called Child's Binomial Theorem. (Rofl) 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).

- Sep 6th 2010, 02:58 PMzg12
That's what I thought, only n=1. Thanks

- Sep 6th 2010, 03:30 PMundefined
Also of course when x=0 or y=0.