Certainly! Let's use the distributive property to write an equivalent expression for [tex]\( 8(7r + 2s - 6) \)[/tex].
### Step-by-Step Solution:
1. Understand the Expression:
We need to distribute the number 8 to each term inside the parentheses, which are [tex]\(7r\)[/tex], [tex]\(2s\)[/tex], and [tex]\(-6\)[/tex].
2. Apply the Distributive Property:
The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex]. In this case, we apply this property to each term inside the parentheses:
- [tex]\( 8 \cdot (7r) \)[/tex]
- [tex]\( 8 \cdot (2s) \)[/tex]
- [tex]\( 8 \cdot (-6) \)[/tex]
3. Perform the Multiplications:
Multiply 8 by each term separately:
- [tex]\( 8 \cdot 7r = 56r \)[/tex]
- [tex]\( 8 \cdot 2s = 16s \)[/tex]
- [tex]\( 8 \cdot (-6) = -48 \)[/tex]
4. Combine the Results:
Combine the results from each multiplication to form the equivalent expression:
[tex]\[
56r + 16s - 48
\][/tex]
So, the equivalent expression for [tex]\(8(7r + 2s - 6)\)[/tex] using the distributive property is [tex]\( 56r + 16s - 48 \)[/tex].
