因式分解:x^4+y^4+（x+y）^4不要在百度上搜的自己做

Question

因式分解:x^4+y^4+（x+y）^4
不要在百度上搜的 自己做

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