Đáp án+Giải thích các bước giải:
`a)x^8+x^4+1`
`=x^8+2x^4+1-x^4`
`=(x^4+1)^2-(x^2)^2`
`=(x^4-x^2+1)(x^4+x^2+1)`
`=(x^4-x^2+1)(x^4+2x^2+1-x^2)`
`=(x^4-x^2+1)[(x^2+1)^2-x^2]`
`=(x^4-x^2+1)(x^2-x+1)(x^2+x+1)`
`b)x^4+6x^3+13x^2+12x+4`
`=x^4+4x^3+4x^2+2x^3+8x^2+8x+x^2+4x+4`
`=x^2(x^2+4x+4)+2x(x^2+4x+4)+x^2+4x+4`
`=(x^4+4x+4)(x^2+2x+1)`
`=(x+2)^2(x+1)^2`
`c)x^11+x^10+......+x^2+x+1`
`=x^10(x+1)+x^8(x+1)+.......+x^2(x+1)+x+1`
`=(x+1)(x^10+x^8+....+x^2+1)`
`=(x+1)[x^8(x^2+1)+x^4(x^2+1)+x^2+1]`
`=(x+1)(x^2+1)(x^8+x^4+1)`
`=(x+1)(x^2+1)(x^8+2x^4+1-x^4)`
`=(x+1)(x^2+1)[(x^4+1)^2-(x^2)^2]`
`=(x+1)(x^2+1)(x^4-x^2+1)(x^4+x^2+1)`
`=(x+1)(x^2+1)(x^4-x^2+1)(x^4+2x^2+1-x^2)`
`=(x+1)(x^2+1)(x^4-x^2+1)[(x^2+1)^2-x^2]`
`=(x+1)(x^2+1)(x^4-x^2+1)(x^2-x+1)(x^2+x+1)`
`d)(x+y)(x+2y)(x+3y)(x+4y)+y^4`
`=[(x+y)(x+4y)][(x+2y)(x+3y)]+y^4`
`=(x^2+5xy+4y^2)(x^2+5xy+6y^2)+y^4`
`=(x^2+5xy+4y^2)(x^2+5xy+4y^2+2y^2)+y^4`
`=(x^2+5xy+4y^2)^2+2y^2(x^2+5xy+4y^2)^2+y^4`
`=(x^2+5xy+4y^2+y^2)^2`
`=(x^2+5xy+5y^2)^2`
