d: \(48x^3y^3-32x^2y^2\)
\(=16x^2y^2\cdot3xy-16x^2y^2\cdot2\)
\(=16x^2y^2\left(3xy-2\right)\)
e: \(9x^2-6x+1=\left(3x\right)^2-2\cdot3x\cdot1+1^2=\left(3x-1\right)^2\)
f: \(x^3-9x+2x^2y+xy^2\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-9\right]\)
\(=x\left(x+y+3\right)\left(x+y-3\right)\)
g: \(3x^2y-9xy^2+12x^2y^2\)
\(=3xy\cdot x-3xy\cdot3y+3xy\cdot4xy\)
\(=3xy\left(x-3y+4xy\right)\)
h: \(x^3-6x^2y+12xy^2-8y^3\)
\(=x^3-3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2-\left(2y\right)^3\)
\(=\left(x-2y\right)^3\)
i: \(3x^3+xy-12xy^2-2y^2\)
\(=3x^3-12xy^2+xy-2y^2\)
\(=3x\left(x^2-4y^2\right)+y\cdot\left(x-2y\right)\)
\(=3x\left(x-2y\right)\left(x+2y\right)+y\left(x-2y\right)\)
\(=\left(x-2y\right)\cdot\left(3x^2+6xy+y\right)\)