Sure, let's work through this step-by-step.
1. Start with the given expression:
[tex]\[
(m - 3 + 4n) \cdot (-8)
\][/tex]
2. Apply the distributive property. The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex]. In this case, we need to distribute the [tex]\(-8\)[/tex] to each term inside the parentheses.
3. Distribute [tex]\(-8\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(-8\)[/tex] by [tex]\(m\)[/tex]:
[tex]\[
-8 \cdot m = -8m
\][/tex]
- Multiply [tex]\(-8\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-8 \cdot (-3) = 24
\][/tex]
- Multiply [tex]\(-8\)[/tex] by [tex]\(4n\)[/tex]:
[tex]\[
-8 \cdot 4n = -32n
\][/tex]
4. Combine all the distributed terms:
[tex]\[
-8m + 24 - 32n
\][/tex]
Therefore, the equivalent expression after applying the distributive property is:
[tex]\[
-8m + 24 - 32n
\][/tex]
