1.x²-y²+a²-b²+2ax+2by
=x²+a²+2ax-y²-b²+2by
=(x+a)^2-(y-b)^2
=(x+a+y-b)(x+a-y+b)
2.a²-4ab+4b²-6a+12b+9
=a²-4ab+4b²-6(a-2b)+9
=(a-2b)^2-6(a-2b)+9
=(a-2b-3)^2
1.8a^3-b^3
=(2a-b)(4a^2+2ab+b^2)
2.4（x-y+1)+y(y-2x)
=4x-4y+4+y^2-2xy
=(y^2-4y+4)-2x(2-y)
=(y-2)^2+2x(y-2)
=(y-2)(2x+y-2)
3.a³+1
=(a+1)(a^2-a+1)
4.4x(四次方)-13x²+9
=(4x^2-9)(x^2-1)
=(2x-3)(2x+3)(x-1)(x+1)
5.b²+c²+2ab+2ac+2bc
=b²+c²+2bc+2ab+2ac
=(b+c)^2+2a(b+c)
=(b+c)(b+c+2a)
6.3x²+5xy-2y²+x+9y-4
=3x^2+5xy-2y^2+x+9y-4
=(x+2y)(3x-y)+x+9y-4
=(x+2y)(3x-y)+4(x+2y)-(3x-y)-4
=(x+2y-1)(3x-y+4)