`a)5x²z-15xyz+30xz²`
`=5xz(x-3y+6z)`
`b)5x²-5xy-10x+10y`
`=(5x²-5xy)-(10x-10y)`
`=5x(x-y)-10(x-y)`
`=(x-y)(5x-10)`
`=5(x-y)(x-2)`
`e)4x(x-3y)+12y(3y-x)`
`=4x(x-3y)-12y(x-3y)`
`=(x-3y)(4x-12y)`
`=4(x-3y)(x-3y)`
`=4(x-3y)^2`
`h)16x²-y²`
`=(4x)²-y²`
`=(4x+y)(4x-y)`
`k)6x²-x-2`
`=6x²+3x-4x-2`
`=(6x²+3x)-(4x+2)`
`=3x(2x+1)-2(2x+1)`
`=(2x+1)(3x-2)`
`p)(x+2)²-x²+2x-1`
`=(x+2)²-(x²-2x+1)`
`=(x+2)²-(x-1)²`
`=[(x+2)+(x-1)][(x+2)-(x-1)]`
`=(x+2+x-1)(x+2-x+1)`
`=(2x+1).3`
`=3(2x+1)`
`o**)(x+2)(x+3)(x+4)(x+5)-24`
`=[(x+2)(x+5)][(x+3)(x+4)]-24`
`=(x²+5x+2x+10)(x²+4x+3x+12)-24`
`=(x²+7x+10)(x²+7x+12)-24`
Đặt `x²+7x+11=a` khi đó ta được:
`(a-1)(a+1)-24`
`=a²-1-24`
`=a²-25`
`=a²-5²`
`=(a+5)(a-5)`
`=(x²+7x+11+5)(x²+7x+11-5)`
`=(x²+7x+16)(x²+7x+6)`
`=(x²+7x+16)(x²+6x+x+6)`
`=(x²+7x+16)[x(x+6)+(x+6)]`
`=(x²+7x+16)(x+6)(x+1)`
`c)1+27x³`
`=27x³+1`
`=(3x)³+1³`
`=(3x+1)[(3x)²-3x.1+1²]`
`=(3x+1)(9x²-3x+1)`
`d)25-a²-2ab-b²`
`=25-(a²+2ab+b²)`
`=5²-(a+b)²`
`=[5+(a+b)][5-(a+b)]`
`=(5+a+b)(5-a-b)`
`t)(x-3)²-(2x+1)²`
`=[(x-3)+(2x+1)][(x-3)-(2x+1)]`
`=(x-3+2x+1)(x-3-2x-1)`
`=(3x-2)(-x-4)`
`=-(3x-2)(x+4)`
`o)(x-2)^2-2(x-2)(2x+1)+(2x+1)^2`
`=[(x-2)-(2x+1)]^2`
`=(x-2-2x-1)^2`
`=(-x-3)^2`
`h)-x^2+3x+10`
`=-x^2+5x-2x+10`
`=(-x^2+5x)-(2x-10)`
`=-x(x-5)-2(x-5)`
`=(x-5)(-x-2)`
`=-(x-5)(x+2)`
`q)x^3+4x^2+4x-4xy^2`
`=x(x^2+4x+4-4y^2)`
`=x[(x^2+4x+4)-4y^2]`
`=x[(x^2+2.x.2+2^2)-(2y)^2]`
`=x[(x+2)^2-(2y)^2]`
`=x(x+2-2y)(x+2+2y)`
`=x(x-2y+2)(x+2y+2)`
`t)x^3-x^2-x+1`
`=(x^3-x^2)-(x-1)`
`=x^2(x-1)-(x-1)`
`=(x-1)(x^2-1)`
`=(x-1)(x^2-1^2)`
`=(x-1)(x-1)(x+1)`
`=(x-1)^2(x+1)`
