Question

(a+b+c)(-a+b+c)(a-b+c)(a+b-c)

Answer 1

(a+b+c)(-a+b+c)(a-b+c)(a+b-c)
=[(b+c)+a][(b+c)-a][a-(b-c)][a+(b-c)]
=[(b+c)²-a²][a²-(b-c)²]
=[(b²+2bc+c²)-a²][a²-(b²-2bc+c²)]
=(b²+2bc+c²-a²)(a²-b²+2bc-c²)
=[2bc-(a²-b²-c²)][2bc+(a²-b²-c²)]
=(2bc)²-(a²-b²-c²)²
=4b²c²-[a²-(b²+c²)]²
=4b²c²-[a的4次方-2a²(b²+c²)+(b²+c²)²]
=4b²c²-(a的4次方-2a²b²-2a²c²+b的4次方+2b²c²+c的4次方)
=4b²c²-a的4次方+2a²b²+2a²c²-b的4次方-2b²c²-c的4次方)
=2b²c²-a的4次方+2a²b²+2a²c²-b的4次方-c的4次方

Answer 2