Bài `4.5`
`a)`
`x(y-z)+y(z-x)+z(x-y)`
`=xy-xz+yz-xy+xz-yz`
`=(xy-xy)+(xz-xz)+(yz-yz)`
`=0`
`b)`
`x(y+z-yz)-y(z+x-zx)+z(y-x)`
`=xy+xz-xyz-yz-xy+xyz+yz-xz`
`=(xy-xy)+(xz-xz)+(xyz-xyz)+(yz-yz)`
`=0`
Bài `4.6`
`a)` Sửa đề : `x^2-x+1 to x^2+x+1`
`(x-1)(x^2+x+1)=x^3+x^2+x-x^2-x-1`
`=x^3+(x^2-x^2)+(x-x)-1`
`=x^3-1`
`b)`
`(x^3+x^2y+xy^2+y^3)(x-y)`
`=[x^2(x+y)+y^2(x+y)](x-y)`
`=(x^2+y^2)(x+y)(x-y)`
`=(x^2+y^2)(x^2-y^2)`
`=x^4-y^4`
Bài `4.7`
`a)`
`(y-5)(y+8)-(y+4)(y-1)`
`=y^2+8y-5y-40-(y^2-y+4y-4)`
`=y^2+3y-40-y^2-3y+4`
`=(y^2-y^2)+(3y-3y)-40+4`
`=-36`
`to đpcm`
`b)`
`y^4-(y^2-1)(y^2+1)`
`=y^4-(y^4-1)`
`=y^4-y^4+1`
`=1`
`to đpcm`