a: \(2xy+5x^2y-x^3y\)
\(=xy\cdot2+xy\cdot5x-xy\cdot x^2\)
\(=xy\left(2+5x-x^2\right)\)
b: \(\left(x+y\right)^2-9x^2\)
\(=\left(x+y\right)^2-\left(3x\right)^2\)
\(=\left(x+y+3x\right)\left(x+y-3x\right)\)
\(=\left(-2x+y\right)\left(4x+y\right)\)
c: \(2\left(x-y\right)+xy-x^2\)
\(=2\left(x-y\right)-\left(x^2-xy\right)\)
\(=2\left(x-y\right)-x\left(x-y\right)\)
\(=\left(x-y\right)\left(2-x\right)\)
d: \(3x^2+2x-1\)
\(=3x^2+3x-x-1\)
\(=\left(3x^2+3x\right)-\left(x+1\right)\)
\(=3x\left(x+1\right)-\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-1\right)\)
e: \(-x^2+4x-3\)
\(=-\left(x^2-4x+3\right)\)
\(=-\left(x^2-x-3x+3\right)\)
\(=-\left[x\left(x-1\right)-3\left(x-1\right)\right]\)
\(=-\left(x-1\right)\left(x-3\right)\)
f: \(x^2-7x+12\)
\(=x^2-3x-4x+12\)
\(=\left(x^2-3x\right)-\left(4x-12\right)\)
\(=x\left(x-3\right)-4\left(x-3\right)\)
=(x-3)(x-4)
g: \(5x\left(x^2-y^2\right)+2y\left(x+y\right)\)
\(=5x\left(x-y\right)\left(x+y\right)+2y\left(x+y\right)\)
\(=\left(x+y\right)\left(5x^2-5xy+2y\right)\)
h: \(x^2-\dfrac{3}{2}x-1\)
\(=\dfrac{1}{2}\left(2x^2-3x-2\right)\)
\(=\dfrac{1}{2}\left(2x^2-4x+x-2\right)\)
\(=\dfrac{1}{2}\left[\left(2x^2-4x\right)+\left(x-2\right)\right]\)
\(=\dfrac{1}{2}\left[2x\left(x-2\right)+\left(x-2\right)\right]\)
\(=\dfrac{1}{2}\left(x-2\right)\left(2x+1\right)\)
i: \(3x+3y-x^2-2xy-y^2\)
\(=\left(3x+3y\right)-\left(x^2+2xy+y^2\right)\)
\(=3\left(x+y\right)-\left(x+y\right)^2\)
\(=\left(x+y\right)\left(3-x-y\right)\)
j: \(x^4y^4+64\)
\(=x^4y^4+16x^2y^2+64-16x^2y^2\)
\(=\left(x^4y^4+16x^2y^2+64\right)-16x^2y^2\)
\(=\left(x^2y^2+8\right)^2-\left(4xy\right)^2\)
\(=\left(x^2y^2-4xy+8\right)\left(x^2y^2+4xy+8\right)\)
k: \(x^3+3x^2y+3xy^2+y^3-x-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
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