27-y3 factored completely = 24
When the expression is broken down into its prime factors it is factored completely.
a3-4a = a(a2-4) when factored
If you mean: y2+5y+6 then it is (y+2)(y+3) when factored completely
A completely factored form is one which is composed of product of factors and can't be factorized further. Let us consider two examples: x2 - 4x + 4 is not a factored form because it can be factored as (x - 2)(x - 2). (x +1)(x2 - 4x + 4) is also not a factored form because x2 - 4x + 4 can be factored further as (x - 2)(x - 2). So, the completely factored form is (x + 1)(x - 2)(x - 2).
77r + 74r - 16 = 151r - 16 and that cannot be factored further.
6p2r(5p2q3 - 3q2 + 7)
12x4 - 42x6 = 6x4 (2 - 7x2)