Question

Answer 1

`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)`

Answer 2

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: \(5x^2y^3-25x^3y^4+10x^3y^3\)

\(=5x^2y^3-5x^2y^3\cdot5xy+5x^2y^3\cdot2x\)

\(=5x^2y^3\left(1-5xy+2x\right)\)