a) \(x^2-10x+9\)
\(=x^2-x-9x+9\)
\(=x\left(x-1\right)-9\left(x-1\right)\)
\(=\left(x-1\right)\left(x-9\right)\)
b) \(3x^2-10xy+3y^2\)
\(=3x^2-xy-9xy+3y^2\)
\(=x\left(3x-y\right)-3y\left(3x-y\right)\)
\(=\left(x-3y\right)\left(3x-y\right)\)
c) \(2x^2-5x+2\)
\(=2x^2-x-4x+2\)
\(=x\left(2x-1\right)-2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x-2\right)\)
d) \(2xy-x^2+3y^2-4y+1\)
\(=-\left(x^2-2xy+y^2\right)+\left(4y^2-4y+1\right)\)
\(=-\left(x-y\right)^2+\left(2y-1\right)^2\)
\(=\left(2y-1\right)^2-\left(x-y\right)^2\)
\(=\left(2y-1-x+y\right)\left(2y-1+x-y\right)\)
\(=\left(3y-x-1\right)\left(x+y-1\right)\)
