(2x-3)(2x+1)(x^2-1)+1
=(2x-3)(2x+1)(x-1)(x+1)+1
=[(2x-3)(x+1)][(2x+1)(x-1)]+1
=(2x^2-x-3)(2x^2-x-1)+1
令2x^2-x=t
=(t-3)(t-1)+1
=t^2-4t+3+1
=(t-2)^2
=(2x^2-x-2)^2
所以(2x-3)(2x+1)(x^2-1)+1是一個完全平方式