Simplify. (x^4+y^5)(x^4-y^5)+y^10

To simplify the expression \((x^{4}+y^{5})(x^{4}-y^{5})+y^{10}\), we can use the difference of squares formula and then combine like terms.<br /><br />First, apply the difference of squares formula to \((x^{4}+y^{5})(x^{4}-y^{5})\):<br /><br />\[<br />(x^{4}+y^{5})(x^{4}-y^{5}) = (x^{4})^2 - (y^{5})^2<br />\]<br /><br />This simplifies to:<br /><br />\[<br />x^{8} - y^{10}<br />\]<br /><br />Now, add \(y^{10}\) to the result:<br /><br />\[<br />x^{8} - y^{10} + y^{10}<br />\]<br /><br />Notice that \(-y^{10}\) and \(+y^{10}\) cancel each other out:<br /><br />\[<br />x^{8} - y^{10} + y^{10} = x^{8}<br />\]<br /><br />Therefore, the simplified expression is:<br /><br />\[<br />\boxed{x^{8}}<br />\]