Sure, let's expand and simplify the expression [tex]\(2(3v + 5)(4v + 1)\)[/tex] step-by-step.
1. Distribute within the parentheses:
First, we expand [tex]\((3v + 5)(4v + 1)\)[/tex] using the distributive property (FOIL method).
[tex]\[
(3v + 5)(4v + 1) = 3v \cdot 4v + 3v \cdot 1 + 5 \cdot 4v + 5 \cdot 1
\][/tex]
2. Perform the multiplications:
[tex]\[
= 12v^2 + 3v + 20v + 5
\][/tex]
3. Combine like terms:
The like terms are [tex]\(3v\)[/tex] and [tex]\(20v\)[/tex].
[tex]\[
= 12v^2 + 23v + 5
\][/tex]
4. Multiply by 2:
Now, we multiply the entire expression [tex]\(12v^2 + 23v + 5\)[/tex] by 2.
[tex]\[
2(12v^2 + 23v + 5) = 2 \cdot 12v^2 + 2 \cdot 23v + 2 \cdot 5
\][/tex]
5. Compute the final expression:
[tex]\[
= 24v^2 + 46v + 10
\][/tex]
So, the expanded and simplified expression for [tex]\(2(3v + 5)(4v + 1)\)[/tex] is:
[tex]\[
24v^2 + 46v + 10
\][/tex]
