Đáp án:
`a, x^4 + 64 = (x^2)^2 + 2.x^2 .8 + 8^2 - 2.x^2 .8`
`= (x^2 + 8)^2 - 16x^2`
`= (x^2 + 8)^2 - (4x)^2`
`= (x^2 + 4x + 8)(x^2 - 4x + 8)`
`b, x^4 + 4y^4 = (x^2)^2 + 2.x^2 .2y^2 + (2y^2)^2 - 2.x^2 .2y^2`
`= (x^2 + 2y^2)^2 - 4x^2 y^2`
`= (x^2 + 2y^2)^2 - (2xy)^2`
`= (x^2 - 2xy + 2y^2)(x^2 + 2xy + 2y^2)`
`c, x^5 + x^4 + 1 = x^5 + x^4 + x^3 - x^3 - x^2 - x + x^2 + x + 1`
`= (x^5 + x^4 + x^3) - (x^3 + x^2 + x) + (x^2 + x + 1)`
`= x^3 (x^2 + x +1) - x(x^2 + x + 1) + (x^2 + x +1)`
`= (x^2 + x + 1)(x^3 - x + 1)`
`C2: x^5 + x^4 + 1 = x^5 - x^2 + x^4 - x + x^2 +x + 1`
`= x^2 (x^3 - 1) + x(x^3 - 1) + (x^2 + x + 1)`
`= x^2 (x - 1)(x^2 + x + 1) + x(x - 1)(x^2 + x + 1) + (x^2 + x + 1)`
`= (x^2 + x + 1)[x^2 (x - 1) + x(x - 1) + 1]`
`= (x^2 +x + 1)(x^3 - x^2 + x^2 - x + 1)`
`= (x^2 + x + 1)(x^3 - x + 1)`
`d, x^8 + x^4 + 1 = x^8 + x^4 + x^4 + 1 - x^4`
`= x^8 + 2x^4 + 1 - x^4`
`= (x^4)^2 + 2.x^4 .1 +1^2 - x^4`
`= (x^4 + 1)^2 - (x^2)^2`
`= (x^4 + x^2 + 1)(x^4 - x^2 +1)`
`= (x^4 + 2x^2 + 1 - x^2)(x^4 - x^2 + 1)`
`=[(x^2)^2 + 2.x^2 .1 + 1^2 - 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)(x^4 - x^2 + 1)`