因式分解:(x+3)(x²-1)(x+5)-9

问题描述:

因式分解:(x+3)(x²-1)(x+5)-9

答:(x+3)(x²-1)(x+5)-9=(x-1)(x+1)(x+3)(x+5)-9=[(x-1)(x+5)]*[(x+1)(x+3)]-9=(x^2+4x-5)(x^2+4x+3)-9=(x^2+4x)^2 -2(x^2+4x)-15-9=(x^2+4x)^2 -2(x^2+4x) -6*4=(x^2+4x-6)(x^2+4x+4)=(x^2+4x-6)(x+2)^2