a)
81-9a^2=9^2-(3a)^2=(9-3a)(9+3a)
b)
16a^2-25=(4a)^2-5^2=(4a-5)(4a+5)
c)
9a^2-16b^2=(3a)^2-(4b)^2=(3a-4b)(3a+4b)
d)
2a^4-18=(\sqrt2a^2)^2-(\sqrt{18})^2=(\sqrt2 a^2-\sqrt{18})(\sqrt2a^2+\sqrt{18})=\\=(\sqrt2 a^2-3\sqrt{2})(\sqrt2a^2+3\sqrt{2})
e)
a^4-7=(a^2)^2-(\sqrt7)^2=(a^2-\sqrt7)(a^2+\sqrt7)
f)
\frac{a^2}{4}-\frac{b^2}{9}=(\frac{a}{2})^2-(\frac{b}{3})^2=(\frac{a}{2}-\frac{b}{3})(\frac{a}{2}+\frac{b}{3})