91Ó°ÊÓ

The distributive property is a fundamental concept in algebra, essential for polynomial multiplication. It says that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products. In this exercise, we used it to distribute each term in the first polynomial, \(6k - 1\), across every term in the second polynomial, \(k^2 + 2k - 4\).
Let's illustrate this with an extra example. Suppose you have \(3(a + b)\). Applying the distributive property, you would multiply \(3\) by each term inside the parentheses, resulting in \(3a + 3b\).
Returning to our problem:

• First, we multiply \(6k\) by each term in \(k^2 + 2k - 4\) to get \(6k^3 + 12k^2 - 24k\).
• Second, we multiply \(-1\) by each term in \(k^2 + 2k - 4\) to get \(-k^2 - 2k + 4\).

Mastering this property allows you to expand and simplify polynomials efficiently.

Once you've distributed and expanded all parts of your polynomials, the next step is to combine like terms. Like terms are terms that contain the same variables raised to the same power. They can be combined by adding or subtracting their coefficients.
For instance, in the simplified terms \(6k^3 + 12k^2 - 24k - k^2 - 2k + 4\), you can combine:

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