因式分解(x-2)(x-3)(x-8)(x-12)-4x^2_数学解答

因式分解(x-2)(x-3)(x-8)(x-12)-4x^2

人气：146 ℃　时间：2020-02-03 03:49:50

解答

原式=[(x-2)(x-12)][(x-3)(x-8)]-4x²
=[(x²+24)-14x][(x²+24)-11x]-4x²
=(x²+24)²-25x(x²+24)+154x²-4x²
=(x²+24)²-25x(x²+24)+150x²
=(x²+24-15x)(x²+24-10x)
=(x²-15x+24)(x-4)(x-6)