Question: User: ๐(๐ฅ) = (๐ฅ โ 1) ยท (๐ฅ + 1) ยท (๐ฅ + 5)
1. **State the problem:**
We are given the function $$f(x) = (x - 1) \cdot (x + 1) \cdot (x + 5)$$ and we want to simplify or expand it.
2. **Formula and rules:**
To expand a product of polynomials, we use the distributive property (also called FOIL for binomials) step by step.
3. **Step 1: Expand the first two factors:**
$$ (x - 1)(x + 1) = x^2 + x - x - 1 = x^2 - 1 $$
4. **Step 2: Multiply the result by the third factor:**
$$ (x^2 - 1)(x + 5) = x^2(x + 5) - 1(x + 5) $$
5. **Step 3: Distribute each term:**
$$ = x^3 + 5x^2 - x - 5 $$
6. **Final answer:**
$$ f(x) = x^3 + 5x^2 - x - 5 $$
This is the expanded form of the given function.