Using binomial theorem, expand `{(x+y)^5+(x-y)^5}dot` and hence find the value of `{(sqrt(2)+1)^5+(sqrt(2)-1)^5}dot`

Explanation

To solve the problem, we will use the Binomial Theorem to expand \((x+y)^5 + (x-y)^5\) and then substitute the values to find \((\sqrt{2}+1)^5 + (\sqrt{2}-1)^5\).

### Step 1: Expand \((x+y)^5\) using the Binomial Theorem
The Binomial Theorem states that:
\[ (a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \]
For \((x+y)^5\):
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