Question

因式分解，急急急.!!!需要过程,谢谢.!

(1)(X2-5X+2)(X2-5X+4)-8

(2)a2*(m+n)3-a2b3

(3)6X2-7X-3

(4)7(a+b)2-5(a+b)-2

(5)3ax-3ay+xy-y2

(6)5x2-15x+2xy-6y

(7)x6-y6-2x3+1

谢谢大家了.要过程.帮忙下.

Answer 1

1``令X^2-5X=t
则原式=（t+2)*(t+4)-8=t^2+4t+2t+8-8=t^2+6t=t*(t+6)
所以，原式=（X^2-5X)(X^2-5X+6)=X(X-5)(X-2)(X-3)

2`` a2*(m+n)3-a2b3
=a^2((m+n)^3-b^3)
=a^2(m+n-b)(m^2+2mn+n^2-mb-nb+b^2)

3``该题主要运用十字相乘：
原式=（3X+1）*（2X-3）

4``令a+b=t
原式=7t^2-5t-2 (又运用十字相乘）
=（7t+2)*(t-1)=(7a+7b+2)*(a+b-1)

5``原式=3a*(x-y)+y*(x-y)=(3a+y)*(x-y)

6``原式=5x(x-3)+2y(x-3)=(x-3)*(5x+2y)

7``原式=（x^6-2x^3+1)-y^6=(x^3-1)^2-y^6=(x^3-1+y^3)*(x^3-1-y^3)

注意：因式分解最重要的是：要有整体代入思想和抽象思维。

Answer 2

(1)(X2-5X+2)(X2-5X+4)-8
=(x*x-5x)(x*x-5x)+6(x*x-5x)+8-8
=(x*x-5x)(x*x-5x+6)
=x(x-5)(x-2)(x-3)
(2)a2*(m+n)3-a2b3
=a2[(m+n)3-b3 ]
=a2(m+n-b)[(m2+2mn+n2+bm+bn+b2)

(3)6X2-7X-3

=(3X+1)(2X-3)

(4)7(a+b)2-5(a+b)-2
=[7(a+b)+2][(a+b)-1]
=(7a+7b+2)(a+b-1)
(5)3ax-3ay+xy-y2
=3a(x-y)+y(x-y)
=(x-y)(3a+y)

(6)5x2-15x+2xy-6y
=5x(x-3)+2y(x-3)
=(x-3)(5x+2y)

(7)x6-y6-2x3+1
=(x3-1)2-y6
=(x3-1+y3)(x3-1-y3)

Answer 3

(1)(X2-5X+2)(X2-5X+4)-8
=(x^2-5x)^2+6(x^2-5x)+8-8
=(x^2-5x)(x^2-5x+6)
=x(x-5)(x-3)(x-2)

(2)a2*(m+n)3-a2b3
=a^2((m+n)^3-b^3)
=a^2(m+n-b)(m^2+2mn+n^2-mb-nb+b^2)

(3)6X2-7X-3
=(3x+1)(2x-3)

(4)7(a+b)2-5(a+b)-2
=(7(a+b)+2)((a+b)-1)
=(7a+7b+2)(a+b-1)

(5)3ax-3ay+xy-y2
=3a(x-y)+y(x-y)
=(3a+y)(x-y)

(6)5x2-15x+2xy-6y
=5x(x-3)+2y(x-3)
=(5x+2y)(x-3)

(7)x6-y6-2x3+1
=(x^3-1)^2-(y^3)^2
=(x^3+y^3-1)(x^3-y^3-1)