Question
Use the Distributive Property to find \( (3 m+1)(m+9) \)
Ask by Hart Curry. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( (3m + 1)(m + 9) = 3m^2 + 28m + 9 \)
Solution
To expand the expression \( (3m + 1)(m + 9) \) using the **Distributive Property**, follow these steps:
### Step 1: Apply the Distributive Property
The Distributive Property states that \( a(b + c) = ab + ac \). When multiplying two binomials, you'll distribute each term in the first binomial to each term in the second binomial.
\[
(3m + 1)(m + 9) = 3m \cdot m + 3m \cdot 9 + 1 \cdot m + 1 \cdot 9
\]
### Step 2: Perform the Multiplications
Calculate each multiplication separately:
1. **First Terms:**
\( 3m \cdot m = 3m^2 \)
2. **Outer Terms:**
\( 3m \cdot 9 = 27m \)
3. **Inner Terms:**
\( 1 \cdot m = m \)
4. **Last Terms:**
\( 1 \cdot 9 = 9 \)
So, the equation becomes:
\[
3m^2 + 27m + m + 9
\]
### Step 3: Combine Like Terms
Combine the \( m \) terms (\( 27m + m \)):
\[
3m^2 + 28m + 9
\]
### Final Answer
\[
(3m + 1)(m + 9) = 3m^2 + 28m + 9
\]
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Simplify this solution The Deep Dive
To solve \( (3m + 1)(m + 9) \) using the Distributive Property, we can distribute each term in the first parenthesis to each term in the second parenthesis. First, distribute \( 3m \): \[ 3m \cdot m = 3m^2 \] \[ 3m \cdot 9 = 27m \] Next, distribute \( 1 \): \[ 1 \cdot m = m \] \[ 1 \cdot 9 = 9 \] Now, combining all these results, we get: \[ 3m^2 + 27m + m + 9 \] Now, combine like terms: \[ 3m^2 + (27m + m) + 9 = 3m^2 + 28m + 9 \] So, \( (3m + 1)(m + 9) = 3m^2 + 28m + 9 \). And there you have it!
