帮忙做几道因式分解1.(x+y+z)^3-x^3-y^3-z^32.a^2+2b^2+3c^2+3ab+4ac+5bc3.(x^2+5x+6)(x^2+7x+6)-3x^24.已知a^2+ab-2^6=13.求整数a,b的值5．设a+b+c=0,a^3+b^3+c^3=0.求a^99+b^99+c^996．x^2+mx+n既是2x^3+3x^2-2x-3的因式,也是x^3+2x^2+(1-

Question

帮忙做几道因式分解
1.(x+y+z)^3-x^3-y^3-z^3
2.a^2+2b^2+3c^2+3ab+4ac+5bc
3.(x^2+5x+6)(x^2+7x+6)-3x^2
4.已知a^2+ab-2^6=13.求整数a,b的值
5．设a+b+c=0,a^3+b^3+c^3=0.求a^99+b^99+c^99
6．x^2+mx+n既是2x^3+3x^2-2x-3的因式,也是x^3+2x^2+(1-a)x+a的因式,求a的值

Answer 1

1.(x+y+z)^3-x^3-y^3-z^3
=[(x+y)+z]^3-x^3-y^3-z^3
=(x+y)^3+3z(x+y)^2+3z^2(x+y)+z^3-x^3-y^3-z^3
=x^3+3x^2*y+3x*y^2+y^3+3z(x^2+2xy+y^2)+3xz^2+3yz^2+z^3-x^3-y^3-z^3
=3x^2*y+3x*y^2+3zx^2+6xyz+3y^2z+3xz^2+3yz^2
=3xy(x+y)+3z(x^2+2xy+y^2)+3z^2(x+y)
=3xy(x+y)+3z(x+y)^2+3z^2(x+y)
=3(x+y)[xy+z(x+y)+z^2]
=3(x+y)(xy+xz+yz+z^2)
=3(x+y)[x(y+z)+z(y+z)]
=3(x+y)(y+z)(x+z).
2.a^2+2b^2+3c^2+3ab+4ac+5bc
=(a+b+c)(a+2b+3c)
3.(x^2+5x+6)(x^2+7x+6)-3x^2
=[(x^2+6)+5x]*[(x^2+6)+7x]-3x^2
=(x^2+6)^2+12x(x^2+6)+35x^2-3x^2
=(x^2+6)^2+12x(x^2+6)+32x^2
=(x^2+6+4x)(x^2+6+8x)
4.已知a^2+ab-2^6=13.求整数a,b的值?
5．设a+b+c=0,a^3+b^3+c^3=0.求a^99+b^99+c^99
a+b+c=0
所以c=-(a+b)
所以c^3=-(a^3+b^3+3a^2b+3ab^2)
所以a^3+b^3+c^3=-3a^2b-3ab^2=0
所以3ab(b+a)=0
所以a+b=0,或者a,b中有一个为零
而当a+b=0时,c=-(a+b)=0
所以a,b,c中至少有一个为0
而其它的2个数相加为0,也即相反数
所以a^99+b^99+c^99 =0
6．x^2+mx+n既是2x^3+3x^2-2x-3的因式,也是x^3+2x^2+(1-a)x+a的因式,求a的值
2x^3+3x^2-2x-3
=(x-1)(x+1)(2x+3)
1):x^2+mx+n是(x+1)(x-1)=x^2-1
x^3+2x^2+(1-a)x+a
=(x^2-1)(x+2)+(2-a)x+a+2
2-a=0,a+2=0,不成立
2)x^2+mx+n是(x+1)(x+3/2)
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