Question

(x+1)(x+3)(x+5)(x+7)+15因式分解答案为(x+2)(x+6)(x+4-根号6)(x+4+根号6）,

Answer 1

(x+1)(x+3)(x+5)(x+7)+15=(x+1)(x+7)(x+3)(x+5)+15

=(x^2+8x+7)(x^2+8x+15)+15

将x^2+8x看做一整体

=(x^2+8x)^2+22(x^2+8x)+120

=(x^2+8x+12)(x^2+8x+10)

=(x+2)(x+6)(x^2+8x+16-6)

=(x+2)(x+6)(x+4-根号6)(x+4+根号6）