`6.`
`a)x^4+x³+x+1`
`=(x^4+x³)+(x+1)`
`=x³(x+1)+(x+1)`
`=(x+1)(x³+1)`
`=(x+1)(x+1)(x²-x+1)`
`=(x+1)²(x²-x+1)`
`b)x^4-x³-x+1`
`=(x^4-x³)-(x-1)`
`=x³(x-1)-(x-1)`
`=(x-1)(x³-1)`
`=(x-1)(x-1)(x²+x+1)`
`=(x-1)²(x²+x+1)`
`c)x²y+xy²-x-y`
`=(x²y+xy²)-(x+y)`
`=xy(x+y)-(x+y)`
`=(x+y)(xy-1)`
`d)` Sửa đề:`ax²+a²y-7x-7y`
`→a²x+a²y-7x-7y`
`a²x+a²y-7x-7y`
`=(a²x+a²y)-(7x+7y)`
`=a²(x+y)-7(x+y)`
`=(x+y)(a²-7)`
`=(x+y)[a^2-(`$\sqrt[]{7}$ `)^2]`
`=(x+y)(a+`$\sqrt[]{7}$`)(a-`$\sqrt[]{7}$`)`
`e)ax²+ay-bx²-by`
`=(ax²+ay)-(bx²+by)`
`=a(x²+y)-b(x²+y)`
`=(x²+y)(a-b)`
`f)x(x+1)²+x(x-5)-5(x+1)²`
`=[x(x+1)²-5(x+1)²]+x(x-5)`
`=(x+1)²(x-5)+x(x-5)`
`=(x-5)[(x+1)²+x]`
`=(x-5)(x²+2x+1+x)`
`=(x-5)(x²+3x+1)`
`7.`
`a)3x²-12y²`
`=3(x²-4y²)`
`=3[x²-(2y)²]`
`=3(x+2y)(x-2y)`
`b)5xy²-10xyz+5xz²`
`=5x(y²-2yz+z²)`
`=5x(y-z)²`
`c)x³+3x²+3x+1-27z³`
`=(x³+3x²+3x+1)-27z³`
`=(x+1)³-(3z)³`
`=(x+1-3z)[(x+1)²+3z(x+1)+(3z)²]`
`=(x-3z+1)(x²+2x+1+3xz+3z+9z²)`
`8.`
`a)x²-2xy+y²-xz+yz`
`=(x²-2xy+y²)-(xz-yz)`
`=(x-y)²-z(x-y)`
`=(x-y)(x-y-z)`
`b)x²-y²-x+y`
`=(x²-y²)-(x-y)`
`=(x+y)(x-y)-(x-y)`
`=(x-y)(x+y-1)`
`c)a³x-ab+b-x`
`=(a³x-x)-(ab-b)`
`=x(a³-1)-b(a-1)`
`=x(a-1)(a²+a+1)-b(a-1)`
`=(a-1)[x(a²+a+1)-b]`
`=(a-1)(a²x+ax+x-b)`
`d)a³x-ab+b-x`
`=(a³x-x)-(ab-b)`
`=x(a³-1)-b(a-1)`
`=x(a-1)(a²+a+1)-b(a-1)`
`=(a-1)[x(a²+a+1)-b]`
`=(a-1)(a²x+ax+x-b)`
`e)3x²(a+b+c)+36xy(a+b+c)+108y²(a+b+c)`
`=(a+b+c)(3x²+36xy+108y²)`
`=3(a+b+c)(x²+12xy+36y²)`
`=3(a+b+c)[x²+2.x.6y+(6y)²]`
`=3(a+b+c)(x+6y)²`
