Đáp án:
`A=(x+y+z)(x+y-z)`
`B=(y-x)(y-z)(x-z)`
`C=(x-y)(y-z)(x-z)`
`D=3(a+b)(b+c)(a-c)`
Giải thích các bước giải:
`A=x²+(2x+y)y-z²`
`=x²+2xy+y²-z²`
`=(x²+2xy+y²)-z²`
`=(x+y)²-z²`
`=(x+y+z)(x+y-z)`
`B=x(y²-z²)+y(z²-x²)+z(x²-y²)`
`=xy²-xz²+yz²-x²y+z(x+y)(x-y)`
`=(xy²-x²y)+(yz²-xz²)-z(x+y)(y-x)`
`=xy(y-x)+z²(y-x)-z(x+y)(y-x)`
`=(y-x)[xy+z²-z(x+y)]`
`=(y-x)(xy+z²-xz-yz)`
`=(y-x)[(xy-xz)-(yz-z²)]`
`=(y-x)[x(y-z)-z(y-z)]`
`=(y-x)(y-z)(x-z)`
`C=xy(x-y)+yz(y-z)+xz(z-x)`
`=xy(x-y)+y²z-yz²+xz²-x²z`
`=xy(x-y)-(x²z-y²z)+(xz²-yz²)`
`=xy(x-y)-z(x²-y²)+z²(x-y)`
`=xy(x-y)-z(x+y)(x-y)+z²(x-y)`
`=(x-y)[xy-z(x+y)+z²]`
`=(x-y)(xy-xz-yz+z²)`
`=(x-y)[(xy-xz)-(yz-z²)]`
`=(x-y)[x(y-z)-z(y-z)]`
`=(x-y)(y-z)(x-z)`
`D=(a+b)³+(c-a)³-(b+c)³`
`=a³+3a²b+3ab²+b³+c³-3ac²+3a²c-a³-(b³+3b²c+3bc²+c³)`
`=a³+3a²b+3ab²+b³+c³-3ac²+3a²c-a³-b³-3b²c-3bc²-c³`
`=(a³-a³)+3a²b+3ab²+(b³-b³)+(c³-c³)-3ac²+3a²c-3b²c-3bc²`
`=3a²b+3ab²-3ac²+3a²c-3b²c-3bc²`
`=3(a²b+ab²-ac²+a²c-b²c-bc²)`
`=3[(a²b+ab²)+(a²c-b²c)-(ac²+bc²)]`
`=3[ab(a+b)+c(a²-b²)-c²(a+b)]`
`=3[ab(a+b)+c(a+b)(a-b)-c²(a+b)]`
`=3(a+b)[ab+c(a-b)-c²]`
`=3(a+b)(ab+ac-bc-c²)`
`=3(a+b)[(ab+ac)-(bc+c²)]`
`=3(a+b)[a(b+c)-c(b+c)]`
`=3(a+b)(b+c)(a-c)`
