(k2−5k−2)(k2+2)

Jasonbradley

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Jun 16, 2024

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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.