Sure! Let's simplify the expression \((3x + 2)^2\) step-by-step.
### Step 1: Write the expression out in expanded form
The given expression is \((3x + 2)^2\).
To expand this, we can use the formula for the square of a binomial:
[tex]\[
(a + b)^2 = a^2 + 2ab + b^2
\][/tex]
Here \(a = 3x\) and \(b = 2\). So, we substitute \(a\) and \(b\) into the formula:
### Step 2: Apply the formula
Let's break it down into parts:
[tex]\[
(3x + 2)^2 = (3x)^2 + 2(3x)(2) + (2)^2
\][/tex]
### Step 3: Compute each term individually
1. First term: \((3x)^2 = 9x^2\)
2. Second term: \(2(3x)(2) = 12x\)
3. Third term: \((2)^2 = 4\)
### Step 4: Combine all terms
Combine all the terms to write the expanded form:
[tex]\[
9x^2 + 12x + 4
\][/tex]
So, the simplified expression for \((3x + 2)^2\) is:
[tex]\[
9x^2 + 12x + 4
\][/tex]
### Step 5: Identify the coefficients
In the expression \(9x^2 + 12x + 4\):
- The coefficient of \(x^2\) is \(9\).
- The coefficient of \(x\) is \(12\).
- The constant term is \(4\).
Therefore, the expanded form of the expression \((3x + 2)^2\) is:
[tex]\[
9x^2 + 12x + 4
\][/tex]
