Question

因式分解：（x^2-1)(x+3)(x+5)-9？

Answer 1

因式分解的结果为(x+2)²(x²+4x-6)，详细过程如图请参考：

Answer 2

(x^2-1)(x+3)(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)-24
=(x^2+4x-6)(x^2+4x+4)
=(x^2+4x-6)(x+2)^2