Factorise completely.

1. Group terms with common factors.

$abc - 3c - 6 + 2ab$

$= abc + 2ab - 3c - 6$

2. Factorise each pair to produce a common bracket.

$abc + 2ab - 3c - 6$

$= ab(c+2) - 3(c+2)$

3. Extract the common binomial factor.

$ab(c+2) - 3(c+2)$

$= (c+2)(ab-3)$

$= (ab-3)(c+2)$

1. Extract the common factor.

$80x^4-5=5(16x^4-1)$

2. Recognise and factorise the difference of two squares.

$5(16x^4-1)=5\big((4x^2)^2-1^2\big)=5(4x^2-1)(4x^2+1)$

3. Factorise the remaining difference of two squares completely.

$4x^2-1=(2x)^2-1^2=(2x-1)(2x+1)$

Hence,
$80x^4-5=5(2x-1)(2x+1)(4x^2+1)$.