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 it or understand its expanded form.
2. **Recall the formula:** The product of two binomials $$ (x - 1)(x + 1) $$ is a difference of squares:
$$ (x - 1)(x + 1) = x^2 - 1^2 = x^2 - 1 $$
3. **Apply the formula:** Substitute this back into the original function:
$$ f(x) = (x^2 - 1)(x + 5) $$
4. **Expand the product:** Use distributive property:
$$ f(x) = x^2 \cdot (x + 5) - 1 \cdot (x + 5) = x^2 x + x^2 \cdot 5 - x - 5 $$
5. **Simplify terms:**
$$ f(x) = x^3 + 5x^2 - x - 5 $$
6. **Final answer:** The expanded form of the function is:
$$ f(x) = x^3 + 5x^2 - x - 5 $$