## Algebra 1: Common Core (15th Edition)

$(x^{2}+y^{2})(x+y)(x-y)$
Recognize that $x^{4}=(x^{2})^{2},$ and $y^{4}=(y^{2})^{2}.$ $x^{4}-y^{4}=$ ...write the difference as $a^{2}-b^{2}$. $(x^{2})^{2}-(y^{2})^{2} =$ ...factor using the rule for a difference of two squares. ($a^{2}-b^{2}=(a+b)(a-b),\quad a=x^{2},\ b=y^{2}$) $=(x^{2}+y^{2})(x^{2}-y^{2})$ ... the first parentheses is a sum of squares. There is no special formula for that. But, the second parentheses contain a difference of two squares... $=(x^{2}+y^{2})(x+y)(x-y)$