If a+b+c=5 and ab+bc+ca=10, then prove that `a^(3)+b^(3)+c^(3)-3abc=-25`.

Explanation

To prove that \( a^3 + b^3 + c^3 - 3abc = -25 \) given that \( a + b + c = 5 \) and \( ab + bc + ca = 10 \), we can follow these steps:

### Step 1: Use the identity for \( a^3 + b^3 + c^3 - 3abc \)

The identity we will use is:
\[ a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc) \]
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