(x+1)(x+3)(x+5)(x+7)-9怎么因式分解啊

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(x+1)(x+3)(x+5)(x+7)-9怎么因式分解啊
(x+1)(x+3)(x+5)(x+7)-9怎么因式分解啊

(x+1)(x+3)(x+5)(x+7)-9怎么因式分解啊
(x+1)(x+3)(x+5)(x+7)-9
=[(x+1)(x+7)][(x+3)(x+5)]-9
=(x^2+8x+7)(x^2+8x+15)-9
=(x^2+8x+7)[(x^2+8x+7)+8]-9
=(x^2+8x+7)^2+8(x^2+8x+7)-9
=[(x^2+8x+7)+3][(x^2+8x+7)+5]
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)

(X+1)(X+3)(X+5)(X+7)-9
=(x+1)(x+7)(x+3)(x+5)-9
=(x^2+8x+7)(x^2+8x+15)-9
令x^2+8x+7=t
(X+1)(X+3)(X+5)(X+7)-9
=(x+1)(x+7)(x+3)(x+5)-9
=(x^2+8x+7)(x^2+8x+15)-9
=t(t+8)-9=t^2+8t-9=(t+9)(t-1)
=(x^2+8x+7+9)(x^2+8x+7-1)
=(x^2+8x+16)(x^2+8x+6)
=(x+4)^2*(x^2+8x+6)

(x+1)(x+3)(x+5)(x+7)=x^4+16x^3+86x^2+176x+105
(x+1)(x+3)(x+5)(x+7)-9=x^4+16x^3+86x^2+176x+96
=(x^2+8x+6)(x-4)^2

x+1)(x+3)(x+5)(x+7)-9怎么因式分解啊
(x+1)(x+3)(x+5)(x+7)-9
=[(x+1)(x+7)][(x+3)(x+5)]-9
=(x^2+8x+7)(x^2+8x+15)-9
=(x^2+8x+7)[(x^2+8x+7)+8]-9
=(x^2+8x+7)^2+8(x^2+8x+7)-9
=[(x^2+8x+7)+3][(x^2+8x+7)+5]
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)

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