Factorize 12r2 - 27y2, Factorize 1 - (a - b)2, Factorize 16x2 - (1 - y)2, Factorize Completely 3 - 12x2

The GCF of 12 and 27 is 3.

Here, $A^2 = 4r^2 \implies A = 2r$ and $B^2 = 9y^2 \implies B = 3y$.

The factored expression is $\boxed{3(2r - 3y)(2r + 3y)}$.

2. Factorize $1 - (a-b)^2$

Here, $A^2 = 1 \implies A = 1$ and $B^2 = (a-b)^2 \implies B = (a-b)$.

The factored expression is $\boxed{(1 - a + b)(1 + a - b)}$.

3. Factorize $16x^2 - (1-y)^2$

Here, $A^2 = 16x^2 \implies A = 4x$ and $B^2 = (1-y)^2 \implies B = (1-y)$.

The factored expression is $\boxed{(4x - 1 + y)(4x + 1 - y)}$.

4. Factorize Completely $3 - 12x^2$

The GCF of 3 and 12 is 3.

Here, $A^2 = 1 \implies A = 1$ and $B^2 = 4x^2 \implies B = 2x$.

The completely factored expression is $\boxed{3(1 - 2x)(1 + 2x)}$.