因式分解 (x+1)(x+3)(x+5)(x+7)+15
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因式分解 (x+1)(x+3)(x+5)(x+7)+15
因式分解 (x+1)(x+3)(x+5)(x+7)+15
因式分解 (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)
1 和4 式结合 2和3式结合
=(x2+8x+7)(x2+8x+15)+15
用y代替x2+8x 则
(y+7)(y+15)+15=y2+22y+120=(y+10)(y+12)
则原式=(x2+8x+10)(x2+8x+12)
x2 是x的平方
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