分解因式(x+1)(x+3)(x+5)(x+7)+15

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分解因式(x+1)(x+3)(x+5)(x+7)+15
分解因式(x+1)(x+3)(x+5)(x+7)+15

分解因式(x+1)(x+3)(x+5)(x+7)+15
(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
=(x^2+8x+7)[(x^2+8x+7)+8]+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=[(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)