（1）3a^2y-3ay+6y(2)-x^2+xy-xz(3)-3ma^3+6ma^2-12ma(4)5x(x-y)+2y(x-y)(5)x(x-y）^2-y(x-y)(6)(2x+y)^2-(x+2y)^2(7)4(2p+3q)^2-(3p-q)^2(8)3ax^2-3ay^2(9)y^2+y+1/4(10)x^2/4+xy+y^2

Question

（1）3a^2y-3ay+6y
(2)-x^2+xy-xz
(3)-3ma^3+6ma^2-12ma
(4)5x(x-y)+2y(x-y)
(5)x(x-y）^2-y(x-y)
(6)(2x+y)^2-(x+2y)^2
(7)4(2p+3q)^2-(3p-q)^2
(8)3ax^2-3ay^2
(9)y^2+y+1/4
(10)x^2/4+xy+y^2

Answer 1

（1）3a^2y-3ay+6y
=3y(a^2-3a+2)
=3y(a-2)(a-1)
(2)-x^2+xy-xz
=-x(x-y+z)
(3)-3ma^3+6ma^2-12ma
=-3ma(a^2-2a+3)
(4)5x(x-y)+2y(x-y)
=(x-y)(5x+2y)
(5)x(x-y）^2-y(x-y)
=(x-y)[x(x-y)-y]
=(x-y)(x^2-xy-y)
(6)(2x+y)^2-(x+2y)^2
=[(2x+y)-(x+2y)][(2x+y)+(x+2y)]
=(x-y)(3x+3y)
=3(x-y)(x+y)
(7)4(2p+3q)^2-(3p-q)^2
=[2(2p+3q)-(3p-q)][2(2p+3q)+(3p-q)]
=(2p+6q-3p+q)(2p+6q+3p-q)
=(7q-p)(5p+5q)
=5(p+q)(7q-p)
(8)3ax^2-3ay^2
=3a(x^2-y^2)
=3a(x-y)(x+y)
(9)y^2+y+1/4
=1/4(4y^+4y+1)
=1/4(2y+1)^2
(10)x^2/4+xy+y^2
=1/4(x^2+4xy+4y^2)
=1/4(x+2y)^2