Question

求解， 如图。谢谢。

Answer 1

(1)3ax-3ay+xy-y^2=3a(x-y)+y(x-y)=(x-y)(3a+y)

(2)8x^3+4x^2-2x-1=4x^2(2x+1)-(2x+1)=(2x+1)(4x^2-1)=(2x+1)^2 (2x-1)

(3)5x^2-15x+2xy-6y=5x(x-3)+2y(x-3)=(x-3)(5x+2y)

(4)4xy+1-4x^2-y^2=1-4x^2+4xy-y^2=1-(2x-y)^2=(1+2x-y)(1-2x+y)

(5)a^4b+a^3b^2-a^2b^3-ab^4=a^3b(a+b)-ab^3(a+b)=ab(a+b)(a^2-b^2)=ab(a+b)^2 (a-b)

(6)x^6-y^6-2x^3+2y^3=(x^3+y^3)(x^3y^3)-2(x^3y^3)=(x^3-y^3)(x^3+y^3-2)=(x-y)(x^2+xy+y^2)(x^3+y^3-2)

(7)x^2(x+1)-y(xy+x)=x(x^2+x)-x(y^2+y)=x(x^2+x-y^2-y)=x{(x^2-y^2)+(x-y)}=x(x-y)(x+y+1)

Answer 2

(1) 3ax-3ay+xy-y^2=3a(x-y)+y(x-y)=(x-y)(3a+y)
(2)8x^3+4x^2-2x-1=4x^2(2x+1)-(2x+1)=(2x+1)(4x^2-1)=(2x+1)(2x+1)(2x-1)
(3)5x^2-15x+2xy-6y=5x(x-3)+2y(x-3)=(x-3)(5x+2y)
(4)4xy+1-4x^2-y^2=1-(2x-y)^2=(1+2x-y)(1-2x+y)
(5)a^4b+a^3b^2-a^2b^3-ab^4= a^3b(a+b)-ab^3(a+b)=(a+b)(a^3b-ab^3)=(a+b)ab(a^2-b^2)
=(a+b)ab(a-b)(a+b)
(6)x^6-y^6-2x3+....
(7)x^2(x+1)-y(xy+x)=x(x^2+x-y^2-y)

Answer 3

楼上强人啊