1.4(a-b)^2-8(b-a)=4(a-b)(a-b+2)
2.若a^2+2a+b^2-4b+5=0,则a=___,b=___.
(a^2+2a+1)+(b^2-4b+4)=0
(a+1)^2+(b-2)^2=0
平方大于等于0,相加等于0,若有一个大于0,则另一个小于0,不成立.
所以两个都等于0
所以a+1=0,b-2=0
a=-1,b=2
3.-6a^2*b+9ab^2-3ab=-3ab(2a-3b+1)
4.3a(x-y)^3-6a(y-x)^2=3a(x-y)^2(x-y-2)
5.3a^5-3a=3a(a^4-1)=3a(a^2+1)(a+1)(a-1)
6.2x^2-8y^2=2(x^2-4y^2)=2(x+2y)(x-2y)
7.4ab-4a^2-b^2=-(2a-b)^2
8.4x^2-16xy+16y^2=4(x-2y)^2
9.2x^2-2x-12=2(x^2-x-6)=2(x-3)(x+2)
10.a^2-b^2-2bc-c^2=a-(b+c)^2=(a+b+c)(a-b-c)
11.a^2+b^2-2ab=(a-b)^2
12.(x^2+1+2x)(x^2+1-2x)=(x+1)^2(x-1)^2
13.(a^2-9)(a^2-4)=(a+3)(a-3)(a+2)(a-2)
14.(x^2+3x)^2-2(x^2+3x)-8=(x^2+3x-4)(x^2+3x+2)=(x+4)(x-1)(x+1)(x+2)
15.(x+2)(x+3)+3x+1=x^2+5x+6+3x+1=x^2+8x+7=(x+7)(x+1)
16.已知a-b=2,b-c=1,求a^2-b^2-c^2-ab-ac-bc的值
a-b=2,b-c=1,相加
a-c=3
a^2+b^2+c^2-ab-bc-ac
=(2a^2+2b^2+2c^2-2ab-2bc-2ac)/2
=[(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ac+c^2)]/2
=[(a-b)^2+(b-c)^2+(a-c)^2]/2
=(4+1+9)/2
=7