Hướng dẫn trả lời:
Ta có: `(x + y)^4 + x^4 + y^4.`
`= (x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4) + x^4 + y^4.`
`= x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4 + x^4 + y^4.`
`= 2x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + 2y^4.`
`= 2.(x^4 + 2x^3y + 3x^2y^2 + 2xy^3 + y^4).`
`= 2.[(x^4 + 2x^2y^2 + y^4) + (2x^3y + 2xy^3) + x^2y^2].`
`= 2.[(x^2 + y^2)^2 + 2xy.(x^2 + y^2) + x^2y^2].`
`= 2.[(x^2 + y^2)^2 + 2.(x^2 + y^2).xy + (xy)^2].`
`= 2.[(x^2 + y^2) + xy]^2.`
`= 2.(x^2 + xy + y^2)^2. (đpcm)`
Vậy `(x+y)^4+x^4+y^4 = 2.(x^2+xy+y^2)^2.`