Question

因式分解:x^4+y^4+（x+y）^4

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Answer 1

x^4+y^4+(x+y)^4
=(x²+y²)²-2x²y²+(x+y)^4
=(x²+y²)²-x²y²+(x+y)^4-x²y²
=(x²+y²+xy)(x²+y²-xy)+[(x+y)²+xy][(x+y)²-xy]
=(x²+y²+xy)(x²+y²-xy)+(x²+y²+3xy)(x²+y²+xy)
=(x²+y²+xy)[(x²+y²-xy)+(x²+y²+3xy)]
=(x²+y²+xy)(2x²+2y²+2xy)
=2(x²+y²+xy)²

Answer 2

x^4+y^4+（x+y）^4
=x^4+y^4+（x^2+2xy+y^2）^2
=x^4+y^4+（x^4+4x^2y^2+y^4+2x^3y+2xy^3+x^2y^2)
=2^4+2^4+5^2y^2+2x^3y+2xy^3

Answer 3

3