Factorise: `64-x ^(2)`

Options

A. `(8+x)(8-x)`
B. `(8-x)(8-x)`
C. `(8+x)(8+x)`
D. none of these

Answer

To factorise the expression \( 64 - x^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Recognize the form**: Notice that \( 64 \) can be expressed as \( 8^2 \). Therefore, we rewrite the expression:
\[ 64 - x^2 = 8^2 - x^2 \]

2. **Identify the difference of squares**: The expression \( 8^2 - x^2 \) is a difference of squares. The difference of squares can be factored using the formula:
\[ a^2 - b^2 = (a + b)(a - b) \]
where \( a = 8 \) and \( b = x \).

3. **Apply the formula**: Substitute \( a \) and \( b \) into the formula:
\[ 8^2 - x^2 = (8 + x)(8 - x) \]

4. **Final answer**: Thus, the factorised form of \( 64 - x^2 \) is:
\[ (8 + x)(8 - x) \]

### Summary:
The factorisation of \( 64 - x^2 \) is \( (8 + x)(8 - x) \).