## Expanding and Simplifying the Expression: (k² - 5k - 2)(k² + 2)

This expression involves multiplying two binomials. We can simplify it by using the distributive property (also known as FOIL method).

**1. Expanding the expression:**

**F**irst: Multiply the first terms of each binomial: k² * k² =**k⁴****O**uter: Multiply the outer terms of the binomials: k² * 2 =**2k²****I**nner: Multiply the inner terms of the binomials: -5k * k² =**-5k³****L**ast: Multiply the last terms of the binomials: -5k * 2 =**-10k****Last:**Multiply the last terms of the binomials: -2 * k² =**-2k²****Last:**Multiply the last terms of the binomials: -2 * 2 =**-4**

**2. Combining like terms:**

Putting all the terms together:

k⁴ - 5k³ + 2k² - 2k² - 10k - 4

Simplifying, we get:

**k⁴ - 5k³ - 10k - 4**

Therefore, the expanded and simplified form of the expression (k² - 5k - 2)(k² + 2) is **k⁴ - 5k³ - 10k - 4**.