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Evaluate the following expression:

[tex]\[ (6a - 4)^2 \][/tex]


Sagot :

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]