Appendix A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 12

$1-2x^{2}$ OR $2x^{2}-1 $

Start with given expression: $|1-2x^{2}|$ Since $1-2x^{2}$ could be positive or negative, the absolute value is either the positive or the negative version of what is inside the absolute value bars: $|1-2x^{2}|=1-2x^{2} $ OR $|1-2x^{2}|=-(1-2x^{2})=2x^{2}-1 $