作业帮因式分解,求大神
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/25 01:26:23
因式分解,求大神
x³-9ax²+27a²x-26a³
=x³-9ax²+27a²x-27a³+a³
=x³+3·(-3a)·x²+3·(-3a)²·x+(-3a)³+a³
=(x-3a)³+a³
=(x-3a+a)[(x-3a)²+a²-a(x-3a)]
=(x-2a)(x²-7ax+4a²+9)
(x+y)⁴+x⁴+y⁴
=(x²+y²+2xy)²+(x²+y²)²-2x²y²
=2(x²+y²)²+4xy(x²+y²)+4x²y²-2x²y²
=2(x²+y²)²+4xy(x²+y²)+2x²y²
=2[(x²+y²)²+2xy(x²+y²)+x²y²]
=2(x²+y²+xy)²
(a+b+c)³-(a³+b³+c³)
=[(a+b+c)³-a³]-(b³+c³)
=[(a+b+c)-a][(a+b+c)²+a²+a(a+b+c)]-(b+c)(b²-bc+c²)
=(b+c)(a²+b²+c²+2ab+2bc+2ca+a²+a²+ab+ac)-(b+c)(b²-bc+c²)
=(b+c)(3a²+b²+c²+3ab+2bc+3ca-b²+bc-c²)
=(b+c)(3a²+3ab+3bc+3ca)
=3(b+c)(a²+ab+bc+ca)
x³+3x²y+3xy²+2y³
=x³+3x²y+3xy²+y³+y³
=(x+y)³+y³
=[(x+y)+y][(x+y)²-y(x+y)+y²]
=(x+2y)(x²+2xy+y²-xy-y²+y²)
=(x+2y)x²+xy+y²)
x³-5x²+9x-6
=x³-2x²-3x²+6x+3x-6
=x²(x-2)-3x(x-2)+3(x-2)
=(x-2)(x²-3x+3)
2x³-13x²+3
=2x³-x²-12x²+6x-6x+3
=x²(2x-1)-6x(2x-1)-3(2x-1)
=(2x-1)(x²-6x-3)
=(2x-1)[(x-3)²-12] /如果不要求实数范围内分解,最后两步不需要.
=(2x-1)(x-3+2√3)(x-3-2√3)
=x³-9ax²+27a²x-27a³+a³
=x³+3·(-3a)·x²+3·(-3a)²·x+(-3a)³+a³
=(x-3a)³+a³
=(x-3a+a)[(x-3a)²+a²-a(x-3a)]
=(x-2a)(x²-7ax+4a²+9)
(x+y)⁴+x⁴+y⁴
=(x²+y²+2xy)²+(x²+y²)²-2x²y²
=2(x²+y²)²+4xy(x²+y²)+4x²y²-2x²y²
=2(x²+y²)²+4xy(x²+y²)+2x²y²
=2[(x²+y²)²+2xy(x²+y²)+x²y²]
=2(x²+y²+xy)²
(a+b+c)³-(a³+b³+c³)
=[(a+b+c)³-a³]-(b³+c³)
=[(a+b+c)-a][(a+b+c)²+a²+a(a+b+c)]-(b+c)(b²-bc+c²)
=(b+c)(a²+b²+c²+2ab+2bc+2ca+a²+a²+ab+ac)-(b+c)(b²-bc+c²)
=(b+c)(3a²+b²+c²+3ab+2bc+3ca-b²+bc-c²)
=(b+c)(3a²+3ab+3bc+3ca)
=3(b+c)(a²+ab+bc+ca)
x³+3x²y+3xy²+2y³
=x³+3x²y+3xy²+y³+y³
=(x+y)³+y³
=[(x+y)+y][(x+y)²-y(x+y)+y²]
=(x+2y)(x²+2xy+y²-xy-y²+y²)
=(x+2y)x²+xy+y²)
x³-5x²+9x-6
=x³-2x²-3x²+6x+3x-6
=x²(x-2)-3x(x-2)+3(x-2)
=(x-2)(x²-3x+3)
2x³-13x²+3
=2x³-x²-12x²+6x-6x+3
=x²(2x-1)-6x(2x-1)-3(2x-1)
=(2x-1)(x²-6x-3)
=(2x-1)[(x-3)²-12] /如果不要求实数范围内分解,最后两步不需要.
=(2x-1)(x-3+2√3)(x-3-2√3)