Question
Find the product. Simplify your answer. \[ (2 v+4)(v-1) \]
Ask by Reyes Burgess. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product simplifies to \(2v^2 + 2v - 4\).
Solution
To find the product of \((2v + 4)(v - 1)\) and simplify the expression, follow these steps:
1. **Distribute each term in the first polynomial to each term in the second polynomial:**
\[
(2v + 4)(v - 1) = 2v \cdot v + 2v \cdot (-1) + 4 \cdot v + 4 \cdot (-1)
\]
2. **Perform the multiplication:**
\[
= 2v^2 - 2v + 4v - 4
\]
3. **Combine like terms:**
\[
2v^2 + (-2v + 4v) - 4 = 2v^2 + 2v - 4
\]
**Final Answer:**
\[
2v^2 + 2v - 4
\]
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Simplify this solution Extra Insights
To find the product of \( (2v + 4)(v - 1) \), we will use the distributive property (also known as the FOIL method for binomials): 1. Multiply the first terms: \( 2v \cdot v = 2v^2 \) 2. Multiply the outer terms: \( 2v \cdot (-1) = -2v \) 3. Multiply the inner terms: \( 4 \cdot v = 4v \) 4. Multiply the last terms: \( 4 \cdot (-1) = -4 \) Now, combine all these results: \[ 2v^2 - 2v + 4v - 4 \] Next, combine like terms: \[ 2v^2 + ( -2v + 4v ) - 4 = 2v^2 + 2v - 4 \] So, the simplified product is: \[ \boxed{2v^2 + 2v - 4} \]
