What is the completely factored form of x^4 - y^4?

1. Check the binomial: x to the fourth is (x squared) squared, and y to the fourth is (y squared) squared, so this is a difference of squares. 2. Factor once as the product of conjugates: (x squared - y squared)(x squared + y squared). 3. Notice the first factor, x squared - y squared, is itself a difference of squares and can be factored again into (x - y)(x + y). 4. The sum of squares x squared + y squared cannot be factored further, so the completely factored form is (x - y)(x + y)(x squared + y squared). _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.4 Factor Special Products_