1.x²y²+1-x²-y²+4xy
=x²y²+2xy+1-(x²-2xy+y²)
=(xy+1)²-(x-y)²
=(xy+1+x-y)(xy+1-x+y)
=(xy+x-y+1)(xy-x+y+1)
2.x²-y²+2x-4y-3
=x²+2x+1-(y²+4y+4)
=(x+1)²-(y+2)²
=(x+1+y+2)(x+1-y-2)
=(x+y+3)(x-y-1)
3.x⁴+x²-2ax-a²+1
=(x⁴+2x²+1)-(x²+2ax+a²)
=(x²+1)²-(x+a)²
=(x²+x+a+1)(x²-x-a+1)
4.(x+y)⁴+x⁴+y⁴
=(x+y)⁴+(x+y)(x)
=(x+y)⁴+x⁴+y⁴+2x²y²-2x²y²
=(x²+y²)²
5.(a+b+c)³-(a³+b³+c³)
=(a+b+c)³-a³-(b³+c³)
=(b+c)[(a+b+c)²+a(a+b+c)+a²]-(b+c)(b²-bc+c²)
=(b+c)[(a+b+c)²+a(a+b+c)+a²-b²+bc-c²]
=(b+c)[3a²+3ab+3ac+3bc]
=3(b+c)[a(a+b)+c(a+b)]
=3(b+c)(a+c)(a+b)
=3(a+b)(a+c)(b+c)
未完.