`a)x^3-x`
`=x(x^2-1)=x(x-1)(x+1)`
`b)4x^5y^4-6x^3y^3+10x^2y^2`
`=2x^2y^2(2x^3y^2-3xy+5)`
`c)2x^2y-6xy^3`
`=2xy(x-3y^2)`
`d)5x^2y^3-25x^3y^4+10x^3y^3`
`=5x^2y^3(1-5xy+2x)`
a: \(x^3-x=x\cdot x^2-x\cdot1=x\left(x^2-1\right)=x\left(x-1\right)\left(x+1\right)\)
b: \(4x^5y^4-6x^3y^3+10x^2x^2\)
\(=2x^2y^2\cdot2x^3y^2-2x^2y^2\cdot3xy+2x^2y^2\cdot5\)
\(=2x^2y^2\left(2x^3y^2-3xy+5\right)\)
c: \(2x^2y-6xy^3\)
\(=2xy\cdot x-2xy\cdot3y^2\)
\(=2xy\left(x-3y^2\right)\)
d: \(5x^2y^3-25x^3y^4+10x^3y^3\)
\(=5x^2y^3-5x^2y^3\cdot5xy+5x^2y^3\cdot2x\)
\(=5x^2y^3\left(1-5xy+2x\right)\)