question\nfactor completely.\n1 - x^{2}y^{4}

Explanation:

Step1: Recognize difference - of - squares

The expression $1 - x^{2}y^{4}$ is in the form $a^{2}-b^{2}$, where $a = 1$ and $b=xy^{2}$. The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. So, $1 - x^{2}y^{4}=1^{2}-(xy^{2})^{2}=(1+xy^{2})(1 - xy^{2})$. Since there are no further common factors or ways to factor each of the resulting binomials, we are done.

Answer:

$(1 + xy^{2})(1-xy^{2})$