Question

因式分解，求大神

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Answer 1

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)

Answer 2

x³-9ax²+27a²x-26a³
=x³-9ax²+27a²x-27a³+a³
=(x-3a)³+a³
=(x-3a+a)[(x-3a)²+a(x-3a)+a²]
=(x-2a)(x²-6ax+9a²+ax-3a²+a²)
=(x-2a)(x²-5ax+7a²)

Answer 3

x³-9ax²+27a²x-26a³

= x³-9ax²+27a²x-27a²+a³

=(x-3a)³+ a³

=[(x-3a)+a] [(x-3a)²-a(x-3a)+a²]

=(x-2a)(x²-6ax+9a²-ax+3a²+ a²)

=(x-2a)(x²-7ax+13a²)

(x+y)⁴+x⁴+y⁴

=(x+y)⁴ - x²y²+x⁴+2x²y² +y⁴- x²y²

=[(x+y)²+xy] [(x+y)²-xy］+ (x²+y²)²- x²y²

=(x²+3xy+y²)(x²+xy+y²)+ (x²+xy+y²)(x²-xy+y² )

=(x²++xy+y²)(x²+3xy+y²+x²-xy+y² )

= (x²++xy+y²) (2x²+2xy+2y²)

=2 (x²++xy+y²)²

 

(a+b+c)³-(a³+b³+c³)

=[ (a+b+c)³-a³]- (b³+c³)

= (a+b+c-a)[(a+b+c)²+a (a+b+c) +a²]- (b+c)(b²-bc+c²)

=(b+c)(a²+b²+c²+2ab+2ac+2bc+a²+ab+ac+a²-
b²+bc-c²)

=(b+c)(3a²+3ab+3ac+3bc)

=(b+c)[3a(a+b)+3c(a+b)]

=3(a+b) (a+c) (b+c)

Answer 4

1、x^3-9ax^2+27a^2x-26a^3=(x-2a)(x^2-7ax+13a^2) ，
2、(x+y)^4+x^4+y^4= 2(x^2+xy+y^2)^2 ，
3、(a+b+c)^3-(a^3+b^3+c^3)=3(a+b)(b+c)(c+a) ，
4、x^3+3x^2y+3xy^2+2y^3=(x+2y)(x^2+xy+y^2) ，
5、x^3-5x^2+9x-6=(x-2)(x^2-3x+3) ，
6、2x^3-13x^2+3=(2x-1)(x^2-6x-3) ，