Certainly! To apply the distributive property to create an equivalent expression for [tex]\(5 \times (-2w - 4)\)[/tex], we follow these steps:
1. Understand the distributive property: This property states that for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], the following equation holds:
[tex]\[
a \times (b + c) = (a \times b) + (a \times c)
\][/tex]
In this case, we have [tex]\(a = 5\)[/tex], [tex]\(b = -2w\)[/tex], and [tex]\(c = -4\)[/tex].
2. Apply the distributive property: Multiply the number outside the parentheses (5) by each term inside the parentheses (-2w and -4).
[tex]\[
5 \times (-2w - 4) = (5 \times -2w) + (5 \times -4)
\][/tex]
3. Calculate the products:
- Multiply [tex]\(5\)[/tex] by [tex]\(-2w\)[/tex]:
[tex]\[
5 \times -2w = -10w
\][/tex]
- Multiply [tex]\(5\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
5 \times -4 = -20
\][/tex]
4. Combine the products: Add the results from each multiplication:
[tex]\[
-10w - 20
\][/tex]
So, by applying the distributive property, we find that the equivalent expression for [tex]\(5 \times (-2w - 4)\)[/tex] is:
[tex]\[
-10w - 20
\][/tex]
This is the simplified form of the original expression.
