因式分解1.已知a+b=1,求a^3+b^3+3ab^2+3a^2b的值2.a^3-6a^2b+12ab^2-8b^33

1.已知a+b=1,求a^3+b^3+3ab^2+3a^2b=(a+b)^3=1
2.a^3-6a^2b+12ab^2-8b^3 =(a-2b)^3
3.x^5+x^4+x^3+x^2+x+1=x^4(x+1)+x^2(x+1)+(x+1)=(x+1)(x^4+x^2+1)=(x+1)(x^4+2x^2+1-x^2)=(x+1)((x^2+1)^2-x^2)=(x+1)(x^2+x+1)(x^2-x+1)
4.若x、y为任意有理数,比较6xy和x^2+9y^2大小
x^2+9y^2=x^2+(3y)^2=(x-3y)^2+6xy>=6xy
5.已知a=k+3,b=2k+2,c=3k-1.求a^2+b^2+c^2+2ab-2bc-2ac=(a+b-c)^2=(3k+5-3k+1)^2=36
6.ab(c^2+d^2)+cd(a^2+b^2) =abc^2+abd^2+a^2cd+b^2cd=ac(bc+ad)+bd(ad+bc)=(ac+bd)(bc+ad)
7.(x^2+3x-2)(x^2+3x+4)-16=(x^2+3x)^2+2(x^2+3x)-24=(x^2+3x+12)(x^2+3x-10)=(x^2+3x+12)(x+5)(x-2)

1.a^3+b^3+3ab^2+3a^2b
=(a+b)^3
把a+b=1代入得1^3=1
2.a^3-6a^2b+12ab^2-8b^3
=（a-2b)^3
3.x^5+x^4+x^3+x^2+x+1
=(x^5+x^4)+(x^3+x^2)+(x+1)
=x^4(x+1)+x^2(x+1)+(x+1)
=(x+1)(x^4+x...