因式分解:(6x-1)(4x-1)(3x+1)(x+1)+9x^4

问题描述:

因式分解:(6x-1)(4x-1)(3x+1)(x+1)+9x^4

原式=[(6x-1)(3x+1)][(4x-1)(x+1)]+9x^4=[(3x-1)+18x²][(3x-1)+4x²]+9x^4=(3x-1)²+22x²(3x-1)+81x^4=[(3x-1)+11x²]²-[(2√10)x²]²=[(3x-1)+11x²+(2√10)x²][(3x-1)+11x²-(2√10)x²]=[(11+2√10)x²+3x-1][(11-2√10)x²+3x-1]