The more "complicated" step of giving the compact expression for the sum $\displaystyle\sum_{0\le k\le n}
\binom nka^kb^{n-k}$
is successfully delivered in sage.

```
sage: var('a,b,k,n')
(a, b, k, n)
sage: sum(binomial(n, k)*a^k*b^(n-k), k, 0, n)
(a + b)^n
```

But for the converse step, i do not see the reason to get the expansion (exactly in the form above, not with $a,b$ replaced, using $k$ as a running variable). I never saw this, i never felt the need for this in the given generality. Of course, for explicit, non-variable values of $n$ we can ask for the expansion:

```
sage: ((a + b)^5).expand()
a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5
```

Usually, we are using computer algebra systems (CAS) for a special (mathematical) human purpose, not for implementing all possible operations. Humans have a kind of sense for the progress, and implement then operations that are supporting the progress, thus simplifying an expression, making it more compact, is a wanted operation. Expanding the sum $(a+b)^n$ is not a simple task, since the implementer has to do this only for special cases. (Is the given expression a power? Is the exponent $n$ here, but maybe $n!+2022n(n+1)/2$ somewhere else, integer? Is the base, $a+b$ here, but $abc^7+nb^b$ elsewhere, a binomial? If yes, and this does not happen very often, provide a method `expand_binomial`

maybe for the given expression.) Wanting the method is simple and natural, but implementing it...

What is

`a¨b`

?a typo for

`a+b`

.Sorry...