Đáp án:
`a)(x-1+y)(x-1-y)`
`b)(2x-3+3y)(2x-3-3y)`
`c)(5+2x-y)(5-2x+y)`
`d)(x-y)(3+x-y)`
`e)(x+y)(x+y-z)`
`f)(x-y-1)²`
`g)(x-2y+z-3t)(x-2y-z+3t)`
`h)(x-2y)(x²+2xy+4y²+x-2y)`
Giải thích các bước giải:
`a)x²-2x+1-y²`
`=(x²-2x+1)-y²`
`=(x-1)²-y²`
`=(x-1+y)(x-1-y)`
`b)4x²-12x-9y²+9`
`=(4x²-12x+9)-9y²`
`=[(2x)²-2.2x.3+3²]-9y²`
`=(2x-3)²-(3y)²`
`=(2x-3+3y)(2x-3-3y)`
`c)25-4x²+4xy-y²`
`=25-(4x²-4xy+y²)`
`=25-[(2x)²-2.2x.y+y²]`
`=5²-(2x-y)²`
`=(5+2x-y)(5-2x+y)`
`d)3x-3y+x²-2xy+y²`
`=(3x-3y)+(x²-2xy+y²)`
`=3(x-y)+(x-y)²`
`=(x-y)(3+x-y)`
`e)x²+2xy+y²-xz-yz`
`=(x²+2xy+y²)-(xz+yz)`
`=(x+y)²-z(x+y)`
`=(x+y)(x+y-z)`
`f)x²-2xy+y²-2x+2y+1`
`=(x²-2xy+y²)-(2x-2y)+1`
`=(x-y)²-2(x-y)+1`
`=(x-y-1)²`
`g)x²-4xy+4y²-z²+6zt-9t²`
`=(x²-4xy+4y²)-(z²-6zt+9t²)`
`=[x²-2.x.2y+(2y)²]-[z²-2.z.3t+(3t)²]`
`=(x-2y)²-(z-3t)²`
`=[(x-2y)+(z-3t)][(x-2y)-(z-3t)]`
`=(x-2y+z-3t)(x-2y-z+3t)`
`h)x³-8y³+x²-4xy+4y²`
`=(x³-8y³)+(x²-4xy+4y²)`
`=[x³-(2y)³]+[x²-2.x.2y+(2y)²]`
`=(x-2y)(x²+2xy+4y²)+(x-2y)²`
`=(x-2y)(x²+2xy+4y²+x-2y)`
