4a²c²-(a²-b²+c²)²
=(2ac)²-(a²-b²+c²)²
=(2ac+a²-b²+c²)(2ac-a²+b²-c²)
=[(a²+2ac+c²)-b²][(b²-(a²-2ac+c²)]
=[(a+c)²-b²][b²-(a-c)²]
=(a+c+b)(a+c-b)(b+a-c)(b-a+c)
=(a+b+c)(a-b+c)(a+b-c)(b+c-a)
4a²c²-(a²-b²+c²)²
=(2ac)²-(a²-b²+c²)²
=(2ac+a²-b²+c²)(2ac-a²+b²-c²)
=[(a²+2ac+c²)-b²][(b²-(a²-2ac+c²)]
=[(a+c)²-b²][b²-(a-c)²]
=(a+c+b)(a+c-b)(b+a-c)(b-a+c)
=(a+b+c)(a-b+c)(a+b-c)(b+c-a)