Question
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Answer
\( 3x^2 + 21x + 30 \)
Solution
To multiply the binomials \( (3x + 6)(x + 5) \), you can use the **FOIL** method, which stands for **First**, **Outer**, **Inner**, and **Last**. Here's a step-by-step breakdown:
### Step 1: Apply the FOIL Method
1. **First**: Multiply the first terms in each binomial.
\[
3x \times x = 3x^2
\]
2. **Outer**: Multiply the outer terms in the binomials.
\[
3x \times 5 = 15x
\]
3. **Inner**: Multiply the inner terms in the binomials.
\[
6 \times x = 6x
\]
4. **Last**: Multiply the last terms in each binomial.
\[
6 \times 5 = 30
\]
### Step 2: Combine All the Products
Add all the products from the FOIL method together:
\[
3x^2 + 15x + 6x + 30
\]
### Step 3: Combine Like Terms
Combine the like terms (\(15x\) and \(6x\)):
\[
3x^2 + 21x + 30
\]
### Final Result
The expanded form of \( (3x + 6)(x + 5) \) is:
\[
3x^2 + 21x + 30
\]
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Simplify this solution The Deep Dive
To multiply \( (3x + 6)(x + 5) \), we can use the distributive property, also known as the FOIL method for binomials. This means we will multiply each term in the first binomial by each term in the second binomial. First, we multiply \( 3x \) by each term in \( (x + 5) \): 1. \( 3x \cdot x = 3x^2 \) 2. \( 3x \cdot 5 = 15x \) Next, we multiply \( 6 \) by each term in \( (x + 5) \): 1. \( 6 \cdot x = 6x \) 2. \( 6 \cdot 5 = 30 \) Now, we combine all these results: \[ 3x^2 + 15x + 6x + 30 \] Combine the like terms (\(15x + 6x\)): \[ 3x^2 + 21x + 30 \] So, the final answer is: \[ 3x^2 + 21x + 30 \]
