x^4 y^4 can be factorized as (x^2 y^2)(x^2+y^2) x^4 y^4x+y=(x^2 y^2)(x^2+y^2)(x+y) =(x+y)(x y)(x^2+y^2)x+y =(x y)(x^2+y^2) ...

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Division of a Polynomial by a Polynomial

x4 - y4 ÷ x +...

Question

$x^{4} - y^{4} \div (x + y)$

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Solution

$x^{4} - y^{4}$ can be factorized as $(x^{2} - y^{2}) (x^{2} + y^{2})$

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

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