分解因式4m^3+4m^2n-9mn^2-9n^3 ax^2=ax-bx-b -3x^2-2x^2y^2+6xy (2x^3-4)+(x^2-8x) 4x^2-y^2-4x-2y

题目

分解因式4m^3+4m^2n-9mn^2-9n^3 ax^2=ax-bx-b -3x^2-2x^2y^2+6xy (2x^3-4)+(x^2-8x) 4x^2-y^2-4x-2y
分解因式(1)4m^3+4m^2n-9mn^2-9n^3 (2) ax^2+ax-bx-b (3)x^3y-3x^2-2x^2y^2+6xy (4)(2x^3-4)+(x^2-8x) (5)4x^2-y^2-4x-2y

答案

(1)4m^3+4m^2n-9mn^2-9n^3 =4m^2(m+n)-9n^2(m+n)=(4m^2-9n^2)(m+n)
=(2m-3n)(2m+3m)(m+n)
(2) ax^2+ax-bx-b= ax^2-bx+ax-b=x(ax-b)+(ax-b)=(x+1)(ax-b)
(3)x^3y-3x^2-2x^2y^2+6xy =x^2(xy-3)-2xy(xy-3)=(x^2-2xy)(xy-3)
(4)(2x^3-4)+(x^2-8x)=2x^3+x^2-8x-4=x^2(2x+1)-4x(2x+1)=(x^2-4x)(2x+1)=x(x-4)(2x+1)
(5)4x^2-y^2-4x-2y=(2x-y)(2x+y)-2(2x+y)=(2x-y-2)(2x+y)