Is there a formula for the binomial expansion of $(a-b)^n$?

Question

Like there is a formula for the binomial expansion of $(a+b)^n$ that can be neatly and compactly be written as a summation, does there exist an equivalent formula for $(a-b)^n$ ?

Answer 1

Hint:$$\\ (a+b)^{ n }=\sum _{ k=0 }^{ n }{ \binom{n}{k} { a }^{ n-k } } { b }^{ k }$$ now substitute here $b=-b$ $$(a-b)^{ n }=\sum _{ k=0 }^{ n }{ { \left( -1 \right) }^{ k }\binom{n}{k} { a }^{ n-k } } { b }^{ k }$$

Answer 2

$$(a-b)^n = (a+ (-b))^n = \sum_{k=0}^n \binom{n}{k}a^k (-b)^{n-k} = \sum_{k=0}^n \binom{n}{k}(-1)^{n-k}a^kb^{n-k} = $$