Divide: $x^{4} - y^{4}$ by $x + y$

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Solution

As we know that $a^{2} - b^{2} = (a + b) (a - b)$

Then using this formula we simplify this expression as:

$x^{4} - y^{4} = (x^{2})^{2} - (y^{2})^{2} = (x^{2} + y^{2}) (x^{2} - y^{2}) = (x^{2} + y^{2}) (x + y) (x - y)$

Then dividing the expression by x+y we have:

$\frac{(x^{2} + y^{2}) (x + y) (x - y)}{x + y} = (x^{2} + y^{2}) (x - y)$

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