因式分解 x^2-5x-6 y^2-x-12 (a+b)^3-(a+b) 6a^2b^2-18ab^2c+12ab^2c^2
问题描述:
因式分解 x^2-5x-6 y^2-x-12 (a+b)^3-(a+b) 6a^2b^2-18ab^2c+12ab^2c^2
x^2-5x-6 y^2-x-12 (a+b)^3-(a+b) 6a^2b^2-18ab^2c+12ab^2c^2
答
x^2-5x-6=(x-6)(x+1)
y^2-x-12=(y+3)(y-4)
(a+b)^3-(a+b)=(a+b)[(a+b)^2-1]=(a+b)[(a+b)^2-1^2]=(a+b)(a+b-1)(a+b+1)
6a^2b^2-18ab^2c+12ab^2c^2=6ab^2(a-3c+2c^2)