a: \(2xy+5x^2y-x^3y\)
\(=xy\cdot2+xy\cdot5x-xy\cdot x^2\)
\(=xy\left(2+5x-x^2\right)\)
b: \(2\left(x-y\right)+xy-x^2\)
\(=2\left(x-y\right)-\left(x^2-xy\right)\)
\(=2\left(x-y\right)-x\left(x-y\right)\)
\(=\left(x-y\right)\left(2-x\right)\)
c:
\(3x^2+2x-1\)
\(=3x^2+3x-x-1\)
=3x(x+1)-(x+1)
=(x+1)(3x-1)
d: \(-x^2+4x-3\)
\(=-\left(x^2-4x+3\right)\)
\(=-\left[x^2-x-3x+3\right]\)
\(=-\left[x\left(x-1\right)-3\left(x-1\right)\right]\)
\(=-\left(x-1\right)\left(x-3\right)\)
e: \(x^2-7x+12\)
\(=x^2-3x-4x+12\)
=x(x-3)-4(x-3)
=(x-3)(x-4)
f: \(5x\left(x^2-y^2\right)+2y\left(x+y\right)\)
\(=5x\left(x-y\right)\left(x+y\right)+2y\left(x+y\right)\)
\(=\left(x+y\right)\left(5x^2-5xy+2y\right)\)
g: \(x^2-\dfrac{3}{2}x-1\)
\(=\dfrac{1}{2}\left(2x^2-3x-2\right)\)
\(=\dfrac{1}{2}\left(2x^2-4x+x-2\right)\)
\(=\dfrac{1}{2}\left[2x\left(x-2\right)+\left(x-2\right)\right]\)
\(=\dfrac{1}{2}\left(x-2\right)\left(2x+1\right)\)
h: \(3x+3y-x^2-2xy-y^2\)
\(=\left(3x+3y\right)-\left(x^2+2xy+y^2\right)\)
\(=3\left(x+y\right)-\left(x+y\right)^2\)
\(=\left(x+y\right)\left(3-x-y\right)\)
