百度作业网求①x³+9+3x²+3x.的因式分解.
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/08/11 15:25:34
求①x³+9+3x²+3x.的因式分解.
①x³+9+3x²+3x
②2x²+4xy+2y²-8z²
①x³+9+3x²+3x
②2x²+4xy+2y²-8z²
①x³+9+3x²+3x
=(x³+3x²+3x+1)+8
=(x+1)³+8
=(x+1+2)[(x+1)²+4-2(x+1)]
=(x+3)(x²+3)
②2x²+4xy+2y²-8z²
=2[(x²+2xy+y²)-4z²]
=2[(x+y)²-4z²]
=2(x+y+2z)(x+y-2z)
再问： x^5-x³+x²-1 a²+2ab+b²+2ac+2bc+c² xy-1+x-y （x⁴-x+1）²-3（x²-x）-7 就只有这几题了- -。 求解!!!~
再答： x^5-x³+x²-1 =x³(x²-1)+(x²-1) =(x²-1)(x³+1) =(x+1)(x-1)(x+1)(x²-x+1) =(x+1)²(x-1)(x²-x+1) a²+2ab+b²+2ac+2bc+c² =(a+b+c)² xy-1+x-y =xy+x-(y+1) =x(y+1)-(y+1) =(y+1)(x-1)
=(x³+3x²+3x+1)+8
=(x+1)³+8
=(x+1+2)[(x+1)²+4-2(x+1)]
=(x+3)(x²+3)
②2x²+4xy+2y²-8z²
=2[(x²+2xy+y²)-4z²]
=2[(x+y)²-4z²]
=2(x+y+2z)(x+y-2z)
再问： x^5-x³+x²-1 a²+2ab+b²+2ac+2bc+c² xy-1+x-y （x⁴-x+1）²-3（x²-x）-7 就只有这几题了- -。 求解!!!~
再答： x^5-x³+x²-1 =x³(x²-1)+(x²-1) =(x²-1)(x³+1) =(x+1)(x-1)(x+1)(x²-x+1) =(x+1)²(x-1)(x²-x+1) a²+2ab+b²+2ac+2bc+c² =(a+b+c)² xy-1+x-y =xy+x-(y+1) =x(y+1)-(y+1) =(y+1)(x-1)