The factor of `x ^(2) - 4` are

Options

A. `(x-2), (x-2)`
B. `(x +2) , (x-2)`
C. `(x +2), (x+2)`
D. `(x -4), (x-4)`

Answer

To find the factors of the expression \( x^2 - 4 \), we can use the difference of squares formula. Here’s a step-by-step solution:

### Step 1: Identify the expression
The expression we are given is:
\[ x^2 - 4 \]

### Step 2: Recognize the difference of squares
We can recognize that this expression is a difference of squares. The general form for the difference of squares is:
\[ a^2 - b^2 = (a - b)(a + b) \]
In our case, we can express \( 4 \) as \( 2^2 \). Thus, we can rewrite the expression:
\[ x^2 - 4 = x^2 - 2^2 \]

### Step 3: Apply the difference of squares formula
Now, we can apply the difference of squares formula:
\[ x^2 - 2^2 = (x - 2)(x + 2) \]

### Step 4: Write the final factors
Thus, the factors of the expression \( x^2 - 4 \) are:
\[ (x - 2)(x + 2) \]

### Final Answer
The factors of \( x^2 - 4 \) are \( (x - 2) \) and \( (x + 2) \).

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