Sure, let's simplify the given expression step-by-step!
We are given the following expression to simplify:
[tex]\[
(6d + 1) \cdot (-5)
\][/tex]
### Step 1: Apply the Distributive Property
To simplify this, we need to distribute the [tex]\(-5\)[/tex] to each term inside the parenthesis. The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. Here, [tex]\(a\)[/tex] is [tex]\(-5\)[/tex], [tex]\(b\)[/tex] is [tex]\(6d\)[/tex], and [tex]\(c\)[/tex] is [tex]\(1\)[/tex].
Distributing [tex]\(-5\)[/tex]:
[tex]\[
-5 \cdot (6d) + (-5) \cdot 1
\][/tex]
### Step 2: Perform the multiplication
Next, we perform the multiplication for each term separately.
1. Multiply [tex]\(-5\)[/tex] by [tex]\(6d\)[/tex]:
[tex]\[
-5 \times 6d = -30d
\][/tex]
2. Multiply [tex]\(-5\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
-5 \times 1 = -5
\][/tex]
### Step 3: Combine the results
Now, we combine the terms obtained from the multiplication:
[tex]\[
-30d + (-5)
\][/tex]
### Step 4: Simplify the expression
When combining the terms, we write them together:
[tex]\[
-30d - 5
\][/tex]
Hence, the simplified form of [tex]\((6d + 1) \cdot (-5)\)[/tex] is:
[tex]\[
-30d - 5
\][/tex]
