第1个回答 2010-08-25
提公因式
1.x2-x-y2-y
解法:=(x2-y2)-(x+y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y+1)
2.x3-x2+x-1
解法:=(x3-x2)+(x-1)
=x2(x-1)+(x-1)
=(x-1)(x2+1)
3.5ax+5bx+3ay+3by
解法:=5x(a+b)+3y(a+b)
=(5x+3y)(a+b)
4.ax+ay+bx+by
=x(a+b)+y(a+b)
=(a+b)(x+y)
5.0.73x32-0.32x73
=0.73x32-0.01x32x73
=0.73x32-0.73x32
=0.73x(32-32)
=0
6.3a^2b-6ab^2
=3ab(a-2b)
7. (x+y)^2+x+y
=(x+y)(x+y+1)
8.7y(x-3y)^2+2(x-3y)(x-3y)^2
=(7y+2x-6y)(x-3y)^2
=(2x+y)(x-3y)^2
=1*6=6
9.2a(a+b-c)-2b(c-a-b)-c(b-c+a)
=2a(a+b-c)+2b(a+b-c)-c(a+b-c)
=(a+b-c)(2a+2b-c)
=(a+b-c)[a+b-c+(a+b)]
10.:-2a b+3a +4a
解:-2a b+3a +4a
=-a 2b-a (-3a)-a (-4a )
=-a (2b-3a-4a )
十字相乘
1.x^2+3x-40
=x^2+3x+2.25-42.25
=(x+1.5)^2-(6.5)^2
=(x+8)(x-5).
2.1. 5ax+5bx+3ay+3by
解法:=5x(a+b)+3y(a+b)
=(5x+3y)(a+b)
3.x3-x2+x-1
解法:=(x3-x2)+(x-1)
=x2(x-1)+(x-1)
=(x-1)(x2+1)
4.x2-x-y2-y
解法:=(x2-y2)-(x+y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y+1)
5.2x^3+6x^2+4x
=x(2x+2)(x+2)
6.x^4-6x^2+8
=(x^2-2)(x^2-4)
7.x^4-13x^2+36
=(x^2-4)(x^2-9)
8.(x-2y)^2-2(x-2y)-24
= (x-2y+4)(x-2y-6)
9.7x^2-2xy-5y^2
=(7x+5y)(x-y)
10.2x^3+6x^2+4x
=x(2x+2)(x+2)
公式法
1.25m^2-49n^2
=(5m)2-(7n)2
=(5m-7n)(5m+7n)
2.4x^2y^2-9a^2b^2
=(2xy)2-(3ab)2
=(2xy-3ab)(2xy+3ab)
3.y^2-4x^2
=(y+2x)(y-2x)
4.a^2-4
=(a+2)(a-2)
5.4x^2-1/9
=(2x-1/3)(2x+1/3)
6.x^2-9
=(x+3)(x-3)
7..(4x-3y)2
=(4x)2-2(4x)·(3y)+(3y)2
=16x2-24xy+9y2.
8.(-4xy+ab)2
=(-4xy)2+2(-4xy)·(ab)+(ab)2
=16x2y2-8abxy+a2b2
9.(4a-3b+c)(4a+3b+c)
=[(4a+c)-3b][(4a+c)+3b]
=(4a+c)2-(3b)2
=16a2+8ac+c2-9b2
10.(x-2y+3z)2
=x2+(-2y)2+(3z)2+2·x·(-2y)+2·x·(3z)+2·(-2y)·(3z)
=x2+4y2+9z2-4xy+6xz-12yz.
还有几中方法没有,自己琢磨吧!