Simplify : `(x^(4) - y^(4))/(x^(2) - y^(2))`

Answer

To simplify the expression \((x^{4} - y^{4})/(x^{2} - y^{2})\), we can follow these steps:

### Step 1: Recognize the difference of squares
The expression \(x^{4} - y^{4}\) can be recognized as a difference of squares. We can use the identity:
\[ a^{2} - b^{2} = (a - b)(a + b) \]
Here, let \(a = x^{2}\) and \(b = y^{2}\). Thus, we can rewrite \(x^{4} - y^{4}\) as:
\[ (x^{2})^{2} - (y^{2})^{2} = (x^{2} - y^{2})(x^{2} + y^{2}) \]

### Step 2: Substitute back into the expression
Now, substituting this back into our original expression gives us:
\[ \frac{x^{4} - y^{4}}{x^{2} - y^{2}} = \frac{(x^{2} - y^{2})(x^{2} + y^{2})}{x^{2} - y^{2}} \]

### Step 3: Cancel the common terms
Since \(x^{2} - y^{2}\) appears in both the numerator and the denominator, we can cancel these terms (assuming \(x^{2} \neq y^{2}\)):
\[ = x^{2} + y^{2} \]

### Final Result
Thus, the simplified form of the expression is:
\[ x^{2} + y^{2} \]

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