Bài 9:
`a) x^2-xy+3x-3y=x(x-y)+3(x-y)=(x-y)(x+3)`
`b) x^3-4x^2-xy^2+4x`
`=x(x^2-4x-y^2+4)`
`=x[(x^2-4x+4)-y^2]`
`=x[(x-2)^2-y^2]`
`=x(x-y-2)(x+y-2)`
`c) (x+1)(x+2)(x+3)(x+4)-3`
`=[(x+1)(x+4)][(x+2)(x+3)]-3`
`=(x^2+5x+4)(x^2+5x+6)-3`
`=(x^2+5x+5-1)(x^2+5x+5+1)-3`
`=(x^2+5x+5)^2-1-3`
`=(x^2+5x+5)^2-4`
`=(x^2+5x+5-2)(x^2+5x+5+2)`
`=(x^2+5x+3)(x^2+5x+7)`
`d) x^3-x^2y+5x-5y`
`=x^2(x-y)+5(x-y)`
`=(x-y)(x^2+5)`
`e) x^3-2x^2-9xy^2+x`
`=x(x^2-2x-9y^2+1)`
`=x[(x^2-2x+1)-9y^2]`
`=x[(x-1)^2-(3y)^2]`
`=x(x-3y-1)(x+3y-1)`
`f) (x+2)(X+3)(x+4)(x+5)-24`
`=[(x+2)(x+5)][(x+3)(x+4)]-24`
`=(x^2+7x+10)(x^2+7x+12)-24`
`=(x^2+7x+11-1)(x^2+7x+11+1)-24`
`=(x^2+7x+11)^2-1-24`
`=(x^2+7x+11)^2-25`
`=(x^2+7x+11-5)(x^2+7x+11+5)`
`=(x^2+7x+6)(x^2+7x+16)`
`g) 2x^3+6xy-x^2z-3yz`
`=2x(x^2+3y)-z(x^2+3y)`
`=(x^2+3y)(2x-z)`
`h) x^2-6xy+9y^2-49`
`=(x-3y)^2-7^2`
`=(x-3y-7)(x-3y+7)`
Bài 10:
`a) (3x-2)(4x+5)-6x(2x-1)`
`=12x^2+15x-8x-10-12x^2+6x`
`=13x-10`
`b)(2x-5)^2-4(x+3)(x-3)`
`=4x^2-20x+25-4(x^2-9)`
`=4x^2-20x+25-4x^2+36`
`=61-20x`
`c) (2x^3-5x^2+7x-6):(2x-3)`
`=(2x^3-3x^2-2x^2+3x+4x-6):(2x-3)`
`=[x^2(2x-3)-x(2x-3)+2(2x-3)]:(2x-3)`
`=(2x-3)(x^2-x+2):(2x-3)`
`=x^2-x+2`
