Question
Find the product. Simplify your answer. \[ (3 p+3)(p+4) \]
Ask by Garrett French. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product simplifies to \(3p^2 + 15p + 12\).
Solution
To find the product \((3p + 3)(p + 4)\) and simplify it, follow these steps:
1. **Distribute Each Term:**
Multiply each term in the first binomial by each term in the second binomial:
\[
(3p + 3)(p + 4) = 3p \cdot p + 3p \cdot 4 + 3 \cdot p + 3 \cdot 4
\]
2. **Perform the Multiplications:**
\[
= 3p^2 + 12p + 3p + 12
\]
3. **Combine Like Terms:**
Combine the \(p\) terms (\(12p\) and \(3p\)):
\[
3p^2 + 15p + 12
\]
**Final Simplified Form:**
\[
3p^2 + 15p + 12
\]
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Simplify this solution Mind Expander
To find and simplify the product \( (3p + 3)(p + 4) \), we can use the distributive property, often referred to as the FOIL method for binomials. First, distribute \( 3p \) to both terms inside the second parenthesis: \[ 3p \cdot p + 3p \cdot 4 = 3p^2 + 12p. \] Next, distribute \( 3 \) to both terms inside the second parenthesis: \[ 3 \cdot p + 3 \cdot 4 = 3p + 12. \] Now, combine all these terms together: \[ 3p^2 + 12p + 3p + 12. \] Combine the like terms \( 12p \) and \( 3p \): \[ 3p^2 + 15p + 12. \] Thus, the simplified expression for the product \( (3p + 3)(p + 4) \) is: \[ \boxed{3p^2 + 15p + 12}. \]
