设A=1+2*x的4次方,B=2*x的3次方+x的平方,x是实数,求A.B的大小关系式

第一个求证什么
(1+2x^4)-(2x³+x²)
=1-x²-2x³+2x^4
=(1-x)(1+x)+2x³(x-1)
=(x-1)(2x³-x-1)
=(x-1)[(x³-x)+(x³-1)]
=(x-1)[x(x-1)(x+1)+(x-1)(x²+x+1)]
=(x-1)²(x²+x+x²+x+1)
=(x-1)²(2x²+2x+1/2+1/2)
=(x-1)²[2(x+1/2)²+1/2]
中括号大于0
(x-1)²>=0
所以1+2x^4>=2x³+x²