Certainly! Let's simplify the given expression step by step.
The expression we need to simplify is [tex]\((6a - 4)^2\)[/tex].
### Step 1: Recognize the Binomial Square Formula
The binomial square formula states:
[tex]\[
(x - y)^2 = x^2 - 2xy + y^2
\][/tex]
### Step 2: Identify the Components
In our expression, we identify [tex]\(x\)[/tex] and [tex]\(y\)[/tex] as follows:
[tex]\[
x = 6a \quad \text{and} \quad y = 4
\][/tex]
### Step 3: Apply the Binomial Square Formula
Now, substitute [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the binomial square formula:
[tex]\[
(6a - 4)^2 = (6a)^2 - 2 \cdot 6a \cdot 4 + 4^2
\][/tex]
### Step 4: Calculate Each Term Individually
1. Calculate [tex]\((6a)^2\)[/tex]:
[tex]\[
(6a)^2 = 36a^2
\][/tex]
2. Calculate [tex]\(- 2 \cdot 6a \cdot 4\)[/tex]:
[tex]\[
- 2 \cdot 6a \cdot 4 = -48a
\][/tex]
3. Calculate [tex]\(4^2\)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
### Step 5: Combine the Results
Bring all the parts together:
[tex]\[
(6a - 4)^2 = 36a^2 - 48a + 16
\][/tex]
### Conclusion
Thus, the expanded form of [tex]\((6a - 4)^2\)[/tex] is:
[tex]\[
36a^2 - 48a + 16
\][/tex]
