(k2%2B2).jpeg "(k2−5k−2)(k2+2)")
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:
- First: Multiply the first terms of each binomial: k² * k² = k⁴
- Outer: Multiply the outer terms of the binomials: k² * 2 = 2k²
- Inner: Multiply the inner terms of the binomials: -5k * k² = -5k³
- Last: 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.