`VT=x^4+y^4+(x+y)^4`
`=x^4+y^4+[(x+y)²]²`
`=x^4+y^4+(x²+2xy+y²)²`
`=x^4+y^4+[(x²+y²)+2xy]²`
`=x^4+y^4+(x²+y²)²+2(x²+y²).2xy+(2xy)²`
`=x^4+y^4+(x²)²+2.x².y²+(y²)²+4xy(x²+y²)+4x²y²`
`=x^4+y^4+x^4+2x²y²+y^4+4x³y+4xy³+4x²y²`
`=2x^4+2y^4+6x²y²+4x³y+4xy³`
`=2(x^4+y^4+3x²y²+2x³y+2xy³)`
`=2(x^4+y^4+2x²y²+x²y²+2x³y+2xy³)`
`=2[(x^4+2x²y²+y^4)+(2x³y+2xy³)+x²y²]`
`=2{[(x²)²+2.x².y²+(y²)²]+2(x²+y²).xy+(xy)²}`
`=2[(x²+y²)²+2(x²+y²).xy+(xy)²]`
`=2(x²+y²+xy)²`
Vế trái bằng vế phải đẳng thức được chứng minh
