Question
Find the product. Simplify your answer. \[ (3 p+3)(4 p+4) \] \( \square \)
Ask by Davies Pena. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product simplifies to \(12p^2 + 24p + 12\).
Solution
To find the product of the binomials \((3p + 3)(4p + 4)\) and simplify the expression, follow these steps:
1. **Use the Distributive Property (FOIL Method):**
Multiply each term in the first binomial by each term in the second binomial.
\[
(3p + 3)(4p + 4) = 3p \cdot 4p + 3p \cdot 4 + 3 \cdot 4p + 3 \cdot 4
\]
2. **Perform the Multiplications:**
\[
= 12p^2 + 12p + 12p + 12
\]
3. **Combine Like Terms:**
\[
= 12p^2 + (12p + 12p) + 12
\]
\[
= 12p^2 + 24p + 12
\]
4. **Factor if Necessary (Optional):**
You can factor out a common factor of 12:
\[
= 12(p^2 + 2p + 1)
\]
\[
= 12(p + 1)^2
\]
However, since the problem asks to **simplify**, the expanded form is typically preferred unless factoring provides a more simplified expression based on context.
**Final Answer:**
\[
12p^2 + 24p + 12
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the product of \( (3p + 3)(4p + 4) \), we can start by factoring out the common terms. Notice that \( 3p + 3 \) can be rewritten as \( 3(p + 1) \) and \( 4p + 4 \) can be rewritten as \( 4(p + 1) \). So we have: \[ (3(p + 1))(4(p + 1)) = 3 \cdot 4 \cdot (p + 1)(p + 1) = 12(p + 1)^2 \] Now, expanding \( (p + 1)^2 \) gives us \( p^2 + 2p + 1 \). Thus, the expression becomes: \[ 12(p^2 + 2p + 1) = 12p^2 + 24p + 12 \] So the final simplified answer is: \[ \boxed{12p^2 + 24p + 12} \]
