[tex]\dfrac{4}{16}=\dfrac{4:4}{16:4}=\dfrac{1}{4}\\\\\dfrac{25}{5}=5\\\\\left(\dfrac{4}{16}a^2b^2+\dfrac{25}{5}\right)\left(a^2b^2-\dfrac{1}{2}\right)=\left(\dfrac{1}{4}a^2b^2+5\right)\left(a^2b^2-\dfrac{1}{2}\right)\\\\.\qquad\qquad\dfrac{1}{4}a^2b^2+5\\\underline{.\times\qquad\ \ \ \ \ a^2b^2-\dfrac{1}{2}}\\.\qquad\ \ \ \ -\dfrac{1}{8}a^2b^2-\dfrac{5}{2}\\\underline{+\ \ \dfrac{1}{4}a^4b^4+5a^2b^2\ \ \ \ \ }\\\boxed{\dfrac{1}{4}a^4b^4+4\dfrac{7}{8}a^2b^2-\dfrac{5}{2}}[/tex]
