Certainly! Let's go through the steps to simplify the expression [tex]\(-2(-4u - 2w + 6)\)[/tex] by using the distributive property.
### Step-by-Step Solution:
1. Identify the expression inside the parentheses:
[tex]\[
-4u - 2w + 6
\][/tex]
2. Understand the distributive property:
The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we need to distribute [tex]\(-2\)[/tex] across each term within the parentheses.
3. Distribute [tex]\(-2\)[/tex] to each term in the parentheses separately:
- First term: Distribute [tex]\(-2\)[/tex] to [tex]\(-4u\)[/tex]:
[tex]\[
-2 \cdot -4u = 8u
\][/tex]
- Second term: Distribute [tex]\(-2\)[/tex] to [tex]\(-2w\)[/tex]:
[tex]\[
-2 \cdot -2w = 4w
\][/tex]
- Third term: Distribute [tex]\(-2\)[/tex] to [tex]\(6\)[/tex]:
[tex]\[
-2 \cdot 6 = -12
\][/tex]
4. Combine the results from each distribution:
[tex]\[
8u + 4w - 12
\][/tex]
5. Final simplified expression:
[tex]\[
8u + 4w - 12
\][/tex]
By following these steps, the expression [tex]\(-2(-4u - 2w + 6)\)[/tex] simplifies to:
[tex]\[
8u + 4w - 12
\][/tex]
This is the fully simplified expression using the distributive property.
