x^6+y^6+2x^2y^4+2x^4y^2若X=6,Y=8,它的值是多少

Question

x^6+y^6+2x^2y^4+2x^4y^2
若X=6,Y=8,它的值是多少

Answer 1

设p=x^2,q=y^2
则p+q = 6^2+8^2=100,pq = (6*8)^2 =3^2*2^8=9*256=2304
p^3+q^3 + 2pq(p+q)
=(p+q)(p^2-pq+q^2)+2pq(p+q)
=(p+q)(p^2+pq+q^2)
=(p+q)[(p+q)^2-pq]
=100*(10000-2304)
=769600