Find the product. Simplify your answer. $$ (v+1)(4 v+4) $$

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UpStudy AI · Accepted Answer

To find the product of $$(v + 1)(4v + 4)$$ and simplify the expression, follow these steps:

1. **Use the Distributive Property (FOIL Method):**
   
   Multiply each term in the first parenthesis by each term in the second parenthesis.

$$
   \begin{align*}
   (v + 1)(4v + 4) &= v \cdot 4v + v \cdot 4 + 1 \cdot 4v + 1 \cdot 4 \
   &= 4v^2 + 4v + 4v + 4
   \end{align*}
   $$

2. **Combine Like Terms:**
   
   Add the coefficients of the $$v$$ terms together.

$$
   4v^2 + 4v + 4v + 4 = 4v^2 + 8v + 4
   $$

3. **Final Simplified Form:**
   
   The simplified product is:

$$
   4v^2 + 8v + 4
   $$

**Alternative Factored Form:**

If you prefer to factor the simplified quadratic expression, you can factor out a common term:

$$
4v^2 + 8v + 4 = 4(v^2 + 2v + 1) = 4(v + 1)^2
$$

Both forms are correct, but typically, the expanded form $$4v^2 + 8v + 4$$ is considered the simplified version unless a factored form is specifically requested.

**Answer:**  
After simplifying, the product is $$4v^{2} + 8v + 4$$.
The product simplifies to $$4v^{2} + 8v + 4$$.

Find the product. Simplify your answer. \[ (v+1)(4 v+4) \]

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