Đáp án:
`a)12x`
`b)4xy`
`c)2y(3x²+y²)`
`d)(x+y+z)(x²+y²+z²-xy-yz-xz)`
`e)(y-x)²(x-1)`
`f)(x-y)(x²-3xy+y²)`
Giải thích các bước giải:
`a)(3x+1)²-(3x-1)²`
`=[(3x+1)+(3x-1)][(3x+1)-(3x-1)]`
`=(3x+1+3x-1)(3x+1-3x+1)`
`=6x.2`
`=12x`
`b)(x+y)²-(x-y)²`
`=[(x+y)+(x-y)][(x+y)-(x-y)]`
`=(x+y+x-y)(x+y-x+y)`
`=2x.2y`
`=4xy`
`c)(x+y)³-(x-y)³`
`=[(x+y)-(x-y)][(x+y)²+(x+y)(x-y)+(x-y)²]`
`=(x+y-x+y)(x²+2xy+y²+x²-y²+x²-2xy+y²)`
`=2y(3x²+y²)`
`d)x³+y³+z³-3xyz`
`=x³+y³+z³-3xyz+3x²y-3x²y+3xy²-3xy²`
`=[(x³+3x²y+3xy²+y³)+z³]-(3x²y+3xy²+3xyz)`
`=[(x+y)³+z³]-3xy(x+y+z)`
`=(x+y+z)[(x+y)²-(x+y).z+z²]-3xy(x+y+z)`
`=(x+y+z)[(x+y)²-(x+y).z+z²-3xy]`
`=(x+y+z)(x²+2xy+y²-xz-yz+z²-3xy)`
`=(x+y+z)(x²+y²+z²-xy-yz-xz)`
`e)x(y-x)²-x²+2xy-y²`
`=x(y-x)²-(y²-2xy+x²)`
`=x(y-x)²-(y-x)²`
`=(y-x)²(x-1)`
`f)x(x-y)²-y(x-y)²+xy²-x²y`
`=x(x-y)²-y(x-y)²-(x²y-xy²)`
`=x(x-y)²-y(x-y)²-xy(x-y)`
`=(x-y)[x(x-y)-y(x-y)-xy]`
`=(x-y)(x²-xy-xy+y²-xy)`
`=(x-y)(x²-3xy+y²)`
