Question

分解因式（x+1）（x+3）（x+5）（x+7)-9

Answer 1

（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)^2+22(x^2+8x)+105-9
=(x^2+8x)^2+22(x^2+8x)+96
=(x^2+8x+16)(x^2+8x+6)
=(x+4)^2(x^2+8x+6)

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谢谢

Answer 2

（x+1）（x+3）（x+5）（x+7)-9
= [(x+4)-3][(x+4)+3] [(x+4)-1][(x+4)+1] -9
=[(x+4)^2-9][(x+4)^2-1] -9
=(x+4)^4-10(x+4)^2+9-9
=(x+4)^2((x+4)^2-10)
=(x+4)^2 (x+4-√10) (x+4+√10)

x^2 表示x的平方

Answer 3

（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]^2+22[x^2+8x]+96
=[x^2+8x+6][x^2+8x+16]
=(x^2+8x+6)(x+4)^2