Đáp án:
`a)x²`
`b)-2x²+x-1`
`c)0`
Giải thích các bước giải:
`a)(x-y+z)²+(z-y)²+2(x-y+z)(y-z)`
`=(x-y+z)²+2(x-y+z)(y-z)+(z-y)²`
`=(x-y+z)²+2.(x-y+z).(y-z)+(y-z)²`
`=(x-y+z+y-z)²`
`=x²`
`b)x(x-1)(x-1)-(x+1)(x²-x+1)`
`=x(x-1)²-(x+1)(x²-x.1+1²)`
`=x(x²-2x+1)-(x³+1)`
`=x³-2x²+x-x³-1`
`=(x³-x³)-2x²+x-1`
`=-2x²+x-1`
`c)3x²(x+1)(x-1)-(x²-1)(x^4+x^2+1)+(x^2-1)^3`
`=3x²(x²-1²)-(x^2-1)[(x^2)^2+x².1+1²]+(x^2)^3-3.(x^2)^2 .1+3.x².1²-1³`
`=3x²(x²-1)-[(x^2)^3-1^3]+x^6-3x^4+3x^2-1`
`=3x^4-3x^2-(x^6-1)+x^6-3x^4+3x^2-1`
`=3x^4-3x^2-x^6+1+x^6-3x^4+3x^2-1`
`=(-x^6+x^6)+(3x^4-3x^4)+(-3x^2+3x^2)+(1-1)`
`=0`
