Factorize each of the following expressions : `x^(12)-y^(12)` (ii) `x^9-y^9`

Explanation

Let's solve the given expressions step by step.

### Expression (i): Factorize \( x^{12} - y^{12} \)

1. **Identify the expression**: We have \( x^{12} - y^{12} \).
2. **Recognize the form**: This expression can be recognized as a difference of squares because \( x^{12} \) and \( y^{12} \) can be rewritten as \( (x^6)^2 - (y^6)^2 \).
3. **Apply the difference of squares formula**: The difference of squares formula states that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = x^6 \) and \( b = y^6 \).
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