1: \(6x^2y-12xy^2\)
\(=6xy\cdot x-6xy\cdot2y\)
=6xy(x-2y)
2; \(12x^3y^2z^2-18x^2y^2z^4\)
\(=6x^2y^2z^2\cdot2x-6x^2y^2z^2\cdot3z^2\)
\(=6x^2y^2z^2\left(2x-3z^2\right)\)
3:
\(-4x^2+12x-9\)
\(=-\left(4x^2-12x+9\right)\)
\(=-\left(2x-3\right)^2\)
4: \(x^3-6x^2y+12xy^2-8y^3\)
\(=x^3-3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2-\left(2y\right)^3\)
\(=\left(x-2y\right)^3\)
5: \(5x^2+10xy-4x-8y\)
=5x(x+2y)-4(x+2y)
=(x+2y)(5x-4)
6: \(4x^2-3x-6y+8xy\)
\(=\left(4x^2-3x\right)-\left(6y-8xy\right)\)
\(=x\left(4x-3\right)-2y\left(3-4x\right)\)
\(=\left(4x-3\right)\left(x+2y\right)\)
7: \(8x^2-3x-3y+8xy\)
\(=x\left(8x-3\right)+y\left(8x-3\right)\)
=(8x-3)(x+y)
9: \(x^3-5x=x\cdot x^2-x\cdot5=x\left(x^2-5\right)\)
10: \(4x^2-1+\left(1-2x\right)^2\)
\(=\left(2x-1\right)\left(2x+1\right)+\left(2x-1\right)^2\)
\(=\left(2x-1\right)\left(2x+1+2x-1\right)=4x\left(2x-1\right)\)
11: \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
12: \(4x\left(2y-z\right)+7y\left(z-2y\right)\)
\(=4x\left(2y-z\right)-7y\left(2y-z\right)\)
\(=\left(2y-z\right)\left(4x-7y\right)\)
