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(1)3ax-3ay+xy-y²=3a(x-y)+y(x-y)=(x-y)(3a+y)
(2)8x³+4x²-2x-1=4x²(2x+1)-(2x+1)=(2x+1)(4x²-1)=(2x+1)(4x²-1)=(2x+1)²(2x-1)
(3)5x²-15x+2xy-6y=5x(x-3)+2y(x-3)=(x-3)(5x+2y)
(4)4a²-20ab+25b²-36=(2a)²-2*2*5ab+(5b²)-6²=(2a-5b)²-6²=(2a-5b+6)(2a-5b-6)
(5)4xy+1-4x²-y²=-[(2x)²-2*2xy+y²-1]=-[(2x-y)²-1]=-(2x-y+1)(2x-y-1)
(6)a^4*b+a³b²-a²b³-ab^4
=a³b(a+b)-ab³(a+b)
=(a+b)(a³b-ab³)
=ab(a+b)(a²-b ²)
=ab (a+b)²(a-b)
(7)x^6-y^6-2x³ +1
=x^6-2x³+1-y^6
=(x³-1)²-(y³)²
=(x³+y³-1)(x³-y³-1)
(8)x²(x+1)-y(xy+x)
=x³+x²-xy²-xy
=(x³-xy²)+(x²-xy)
=x(x²-y²)+x(x-y)
=x(x+y)(x-y)+x(x-y)
=x(x-y)(x+y+1)
(2)8x³+4x²-2x-1=4x²(2x+1)-(2x+1)=(2x+1)(4x²-1)=(2x+1)(4x²-1)=(2x+1)²(2x-1)
(3)5x²-15x+2xy-6y=5x(x-3)+2y(x-3)=(x-3)(5x+2y)
(4)4a²-20ab+25b²-36=(2a)²-2*2*5ab+(5b²)-6²=(2a-5b)²-6²=(2a-5b+6)(2a-5b-6)
(5)4xy+1-4x²-y²=-[(2x)²-2*2xy+y²-1]=-[(2x-y)²-1]=-(2x-y+1)(2x-y-1)
(6)a^4*b+a³b²-a²b³-ab^4
=a³b(a+b)-ab³(a+b)
=(a+b)(a³b-ab³)
=ab(a+b)(a²-b ²)
=ab (a+b)²(a-b)
(7)x^6-y^6-2x³ +1
=x^6-2x³+1-y^6
=(x³-1)²-(y³)²
=(x³+y³-1)(x³-y³-1)
(8)x²(x+1)-y(xy+x)
=x³+x²-xy²-xy
=(x³-xy²)+(x²-xy)
=x(x²-y²)+x(x-y)
=x(x+y)(x-y)+x(x-y)
=x(x-y)(x+y+1)
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3ax-3ay+xy-y²
=3a(x-y)+y(x-y)
=(3a+y)(x-y)
=3a(x-y)+y(x-y)
=(3a+y)(x-y)
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(5)原式=1-(4x^2-4xy+y^2)=1-(2x-y)^2=(1+2x-y)(1-2x+y)
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