初一数学问题请教

来源：百度知道 编辑：UC知道 时间：2024/06/08 21:35:06
分解因式：1.（x+3)(x+1)(x+5)(x+7)+15 2.x的平方—8xy+15y方+2x-4y-3
3.x的4次方-2x方y-3y方+8y-4
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1.（x+3)(x+1)(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)

2.x的平方—8xy+15y方+2x-4y-3
x^-8xy+15y^+2x-4y-3
＝x^-8xy+16y^- y^+2x-4y-3
＝(x-4y)^- y^+2y-1-(2y-1)+2x-4y-3
＝(x-4y)^-(y-1)^+2x-6y-2
＝(x-4y-(y-1)) (x-4y+(y-1))+2(x-3y-1)
＝(x-5y+1) (x-3y-1)+2(x-3y-1)
＝(x-5y+1+2) (x-3y-1)
＝(x-5y+3) (x-3y-1)

3.x的4次方-2x方y-3y方+8y-4
x^4-2x^2y-3y^3+8y-4
=x^4-2x^2y+y^2-4y^3+8y-4
=(x^2-y)^2-4(y-1)^2
=[(x^2-y)-2(y-1)][(x^2-y)+2(y-1)]
=(x^2-3y+2)(x^2+y-1)

1 x+3x+1+x+5+x+7+15
=(1+3+1+1)x+(1+5+7+15)
=6x+28