To find the product of the expression [tex]\((t - 3)(3x + 1)\)[/tex], let's go through the steps of expanding this expression.
Given:
[tex]\[
(t - 3)(3x + 1)
\][/tex]
We will use the distributive property to expand this product. The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. Applying this property, we get:
1. Distribute [tex]\(t\)[/tex] to both terms inside the parentheses:
[tex]\[
t \cdot (3x) + t \cdot 1 = 3tx + t
\][/tex]
2. Distribute [tex]\(-3\)[/tex] to both terms inside the parentheses:
[tex]\[
-3 \cdot (3x) + (-3) \cdot 1 = -9x - 3
\][/tex]
3. Combine all the distributed parts:
[tex]\[
3tx + t - 9x - 3
\][/tex]
Therefore, the expanded form of [tex]\((t - 3)(3x + 1)\)[/tex] is:
[tex]\[
3tx + t - 9x - 3
\][/tex]
So, the product of [tex]\((t - 3)(3x + 1)\)[/tex] is:
[tex]\[
3tx + t - 9x - 3
\][/tex]
