分解因式：a^3-2a^2b+ab^2 a^3-a a^2b^2-4 xy^2-6xy+9x m^2-n^2+2m-2n a^2-b^2-2b-1
问题描述：
分解因式：a^3-2a^2b+ab^2 a^3-a a^2b^2-4 xy^2-6xy+9x m^2-n^2+2m-2n a^2-b^2-2b-1
答
a^3-2a^2b+ab^2 a^3-a = a(a^2 - a) = a(a+1)(a-1) a^2b^2-4 = (ab +2)(ab-2) xy^2-6xy+9x = x (y^2 - 6y + 9) = x (y-3)^2 m^2-n^2+2m-2n = (m +n)(m -n) + 2(m-n) = (m + n)(m - n - 2) a^2-b^2-2b-1 = a^2 - (b+1)^2 = (a+b +1)(a - b - 1)