`x^3 - 9x^2 + 18x=0`
⇔ `x ( x^2 - 9x + 18) = 0`
⇔` x (x^2 - 6x - 3x + 18) = 0`
⇔ `x [x ( x -6 ) -3 ( x -6)] = 0`
⇔ `x ( x - 6)(x - 3) = 0`
⇔ `{(x = 0),(x - 6 = 0),(x - 3 = 0):}`
⇔ `{(x = 0),(x = 6),(x = 3:}`
`A= 4x^2 + 2x^2 - 9y^2 + 3xy `
`= 6x^2 - 9y^2 + 3xy`
`= 6x^2 - 6y^2 - 3y^2 + 3xy`
`=6(x^2 - y^2) - 3y(y - x)`
`=6 ( x - y) ( x + y) + 3y( x -y )`
`=3(x-y)[2(x + y) + y]`
`=3(x - y)(2x + 2y + y)`
`=3( x - y )(2x + 3y)`
