Factorise the following completely.

1. Group terms to form common binomial factors

$45b-18ab-2a^2+5a$

$=5a-2a^2+45b-18ab$

2. Extract the common factor from each group

$5a-2a^2+45b-18ab$

$=a(5-2a)+9b(5-2a)$

3. Factorise the common bracket completely

$a(5-2a)+9b(5-2a)$

$=(5-2a)(a+9b)$

1. Factor out the common numerical factor to remove fractions inside the bracket

$2p^2-\frac{2}{3}p-\frac{1}{6}=\frac{1}{6}(12p^2-4p-1)$

2. Factorise the quadratic expression inside the bracket

$12p^2-4p-1=(2p-1)(6p+1)$
Hence,
$2p^2-\frac{2}{3}p-\frac{1}{6}=\frac{1}{6}(2p-1)(6p+1).$