Có: `x=y+2 <=> x-y=2`
Khi đó:
`\qquad 2x^2(x+1)-2y^2(y-1)`
`=2x^3+2x^2-2y^3+2y^2`
`=2(x^3-y^3)+2(x^2+y^2)`
`=2(x-y)(x^2+xy+y^2)+2[(x-y)^2+2xy]`
`=2.2[(x-y)^2+3xy]+2(2^2+2.2)`
`=4(2^2+3.2)+2.(4+4)`
`=4.(4+6)+2.8`
`=4.10+16`
`=56` (1)
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`\qquad x^4+y^4`
`=(x^2+y^2)^2-2x^2y^2`
`=[(x-y)^2+2xy]^2-2(xy)^2`
`=(2^2+2.2)^2-2.2^2`
`=(4+4)^2-8`
`=8^2-8`
`=64-8`
`=56` (2)
Từ (1)(2)`=> (\text{đpcm})`
