To simplify the expression [tex]\(-4(-x + 3)\)[/tex] using the distributive property, we proceed as follows:
1. Apply the distributive property:
The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we have [tex]\(-4\)[/tex] as [tex]\(a\)[/tex], [tex]\(-x\)[/tex] as [tex]\(b\)[/tex], and [tex]\(3\)[/tex] as [tex]\(c\)[/tex].
2. Multiply [tex]\(-4\)[/tex] by each term inside the parentheses:
- Multiply [tex]\(-4\)[/tex] by [tex]\(-x\)[/tex]:
[tex]\[
-4 \cdot (-x) = 4x
\][/tex]
- Multiply [tex]\(-4\)[/tex] by [tex]\(3\)[/tex]:
[tex]\[
-4 \cdot 3 = -12
\][/tex]
3. Combine the results:
After multiplying, you add the two products together:
[tex]\[
4x + (-12) = 4x - 12
\][/tex]
Therefore, the simplified form of the expression [tex]\(-4(-x + 3)\)[/tex] is:
[tex]\[
4x - 12
\][/tex]
