(k%5E2-k-8).jpeg "(k-5)(k^2-k-8)")
Expanding the Expression: (k-5)(k^2-k-8)
This expression involves multiplying a binomial (k-5) with a trinomial (k^2-k-8). We can expand this using the distributive property, also known as FOIL (First, Outer, Inner, Last).
Step 1: Distribute the first term of the binomial.
(k-5)(k^2-k-8) = k(k^2-k-8) - 5(k^2-k-8)
Step 2: Distribute the second term of the binomial.
k(k^2-k-8) - 5(k^2-k-8) = k^3 - k^2 - 8k - 5k^2 + 5k + 40
Step 3: Combine like terms.
k^3 - k^2 - 8k - 5k^2 + 5k + 40 = k^3 - 6k^2 - 3k + 40
Therefore, the expanded form of (k-5)(k^2-k-8) is k^3 - 6k^2 - 3k + 40.
Key Points:
- FOIL Method: This method helps to systematically multiply each term of the first expression with each term of the second expression.
- Distributive Property: This property allows us to multiply a single term by each term within a group.
- Combining like terms: After distribution, we combine terms with the same variable and exponent.
This expanded form is helpful for further algebraic manipulations, solving equations, or understanding the relationship between the original factors and the resulting polynomial.