a: \(4a^2b-6ab^2+16b^2\)
\(=2b\cdot2a^2-2b\cdot3ab+2b\cdot8b\)
\(=2b\left(2a^2-3ab+8b\right)\)
b:
\(4x^2+6xy-1+3y\)
\(=\left(4x^2-1\right)+\left(6xy+3y\right)\)
\(=\left(2x-1\right)\left(2x+1\right)+3y\left(2x+1\right)\)
\(=\left(2x+1\right)\left(2x-1+3y\right)\)