Đáp án+Giải thích các bước giải:
Bài `4:`
`a) (x+y)^3 -1 - 3xy(x+y-1)`
`=(x+y-1)[(x+y)^2 + (x+y) +1]- 3xy(x+y-1)`
`=(x+y-1)(x^2+2xy+y^2+x+y+1-3xy)`
`=(x+y-1)(x^2 -xy +y^2 +x+y)`
`b) x^3 -1 +5x^2 -5 +3x-3`
`=(x-1)(x^2+x+1)+5(x-1)(x+1)+3(x-1)`
`=(x-1)(x^2+x+1+5x+5+3)`
`=(x-1)(x^2 +6x+9)`
`=(x-1)(x+3)^2`
`c) x^3 -3x^2 +3x-1-y^3`
`=(x-1)^2-y^3`
`=(x-1-y)[(x-1)^2+(x-1).y + y^2]`
`=(x-1-y)(x^2-2x+1+xy-y +y^2)`
`d) a^5 +a^4 +a^3 +a^2 +a+1`
`=(a^5+a^4)+(a^3+a^2)+(a+1)`
`=a^4(a+1)+a^2(a+1)+(a+1)`
`=(a+1)(a^4+a^2 +1)`
`=(a+1)(a^4 +2a^2 +1 -a^2)`
`=(a+1)[(a^2+1)^2-a^2]`
`=(a+1)(a^2+1+a)(a^2+1-a)`
`e) 5x^3 -3x^2y -45xy^2 +27y^3`
`=(5x^3 - 45xy^2)-(3x^2y - 27y^3)`
`=5x(x^2 - 9y^2)-3y(x^2 - 9y^2)`
`=(5x-3y)(x^2-9y^2)`
`=(5x-3y)(x-3y)(x+3y)`
`f) 3x^2 (a-b+c)+36xy(a-b+c)+108y^2 (a-b+c)`
`=(a-b+c)(3x^2 +36xy +108y^3)`
`=3(a-b+c)(x^2+12xy +36y^2)`
`=3(a-b+c)[x^2 + 2.x.6y +(6y)^2]`
`=3(a-b+c)(x+6y)^2`
