\[\left( - 2\frac{1}{2} \right)^{2} - \left( 1\frac{1}{4} \right)^{2} =\]
\[= \left( - \frac{5}{2} \right)^{2} - \left( \frac{5}{4} \right)^{2} = \frac{25}{4} - \frac{25}{16} =\]
\[= \frac{75}{16} = 4\frac{11}{16}\]