因式分解难度中等的一些题1.abc+ab+bc+ca+a+b+c+12.x^3+2x^2-5x-63.(x+y)^3-2xy(x+y-1)-4.x^4-4x+35.m^4+64n^4并署名

因式分解难度中等的一些题1.abc+ab+bc+ca+a+b+c+12.x^3+2x^2-5x-63.(x+y)^3-2xy(x+y-1)-4.x^4-4x+35.m^4+64n^4并署名
因式分解难度中等的一些题
1.abc+ab+bc+ca+a+b+c+1
2.x^3+2x^2-5x-6
3.(x+y)^3-2xy(x+y-1)-
4.x^4-4x+3
5.m^4+64n^4
并署名

因式分解难度中等的一些题1.abc+ab+bc+ca+a+b+c+12.x^3+2x^2-5x-63.(x+y)^3-2xy(x+y-1)-4.x^4-4x+35.m^4+64n^4并署名
我发好了

1.(a+1)(b+1)(c+1)
2.(x+1)(x+3)(x-2)
3.没打错吧
4.(x-1)^2 + (x^2 + 2x + 3)
5.(m^2 - 4mn + n^2)(m^2 + 4mn + n^2)

1.abc+ab+bc+ca+a+b+c+1
=ab(c+1)+(bc+b)+(ac+a)+(c+1)
=ab(c+1)+b(c+1)+a(c+1)+(c+1)
=(c+1)(ab+a+b+1)
=(c+1)[a(b+1)+(b+1)]
=(a+1)(b+1)(c+1)
2.x^3+2x^2-5x-6
=(x^3-8)+(2x^2-5x+...

全部展开

1.abc+ab+bc+ca+a+b+c+1
=ab(c+1)+(bc+b)+(ac+a)+(c+1)
=ab(c+1)+b(c+1)+a(c+1)+(c+1)
=(c+1)(ab+a+b+1)
=(c+1)[a(b+1)+(b+1)]
=(a+1)(b+1)(c+1)
2.x^3+2x^2-5x-6
=(x^3-8)+(2x^2-5x+2)
=(x-2)(x^2+2x+4)+(2x-1)(x-2)
=(x-2)(x^2+2x+4+2x-1)
=(x-2)(x^2+4x+3)
=(x-2)(x+1)(x+3)
3.(x+y)^3-2xy(x+y-1)-1
=[(x+y)^3-1]-2xy(x+y-1)
=(x+y-1)[(x+y)^2+(x+y)+1]-2xy(x+y-1)
=(x+y-1)(x^2+2xy+y^2+x+y+1-2xy)
=(x+y-1)(x^2+y^2+x+y+1)
4.x^4-4x+3
=(x^4-1)-(4x-4)
=(x^2+1)(x+1)(x-1)-4(x-1)
=(x-1)(x^3+x^2+x+1-4)
=(x-1)[(x^3-1)+(x^2-1)+(x-1)]
=(x-1)[(x-1)(x^2+x+1)+(x+1)(x-1)+(x-1)]
=(x-1)^2(x^2+x+1+x+1+1)
=(x-1)^2(x^2+2x+3)
5.m^4+64n^4
=m^4+16m^2n^2+64n^4-16m^2n^2
=(m^2+8n^2)^2-16m^2n^2
=(m^2+4mn+8n^2)(m^2-4mn+8n^2)

收起

①=(a+1)(b+1)(c+1)
②=x^3+x^2+x^2-5x-6=X^2(x+1)+(x+1)(x-6)=(x+1)(x+3)(x-2)
③=x^3+y^3+x^2*y+y^2*x+2xy这个题缺了几项，有问题。
④=x^4-x^2+x^2-4x-3=x^2(x+1)(x-1)+(x-3)(x-1)=(x-1)(x^3-x^2+x-3)
⑤无解

不会啊

1： ab(c+1)+b(c+1)+(c+1)+a(c+1)=(c+1)(ab+a+b)
2: x^3+2x^2-3x-2x-6=x^2(x-1)(x+3)-2(x+3)=(x^-2)(x+3)
3:好像没给完全
4：x^4-x^2+x^2-4x+3=x^2(x-1)^2+(x-3)(x-1)=(x^2+x-1)(x-1)
5: m^4+16m^2n^2+64n^4-16m^2n^2=(m^2+n^2)^2-16m^2n^2=(m^2+n^2-4mn)(m^2+n^2+4mn)

(1)原式=(abc+ab)+(ac+a)+(bc+b)+(c+1)
=ab(c+1)+a(c+1)+b(c+1)+(c+1)
=(c+1)(ab+a+b+1)=(a+1)(b+1)(c+1)
(2)原式=x^3-2x^2+4x^2-8x+3x-6
=(x^3-2x^2)+(4x^2-8x)+(3x-6)
...

全部展开

(1)原式=(abc+ab)+(ac+a)+(bc+b)+(c+1)
=ab(c+1)+a(c+1)+b(c+1)+(c+1)
=(c+1)(ab+a+b+1)=(a+1)(b+1)(c+1)
(2)原式=x^3-2x^2+4x^2-8x+3x-6
=(x^3-2x^2)+(4x^2-8x)+(3x-6)
=x^2(x-2)+4x(x-2)+3(x-2)
=(x-2)(x^2+4x+3)=(x-2)(x+1)(x+3)
(3)原式=x^3+y^3+x^2y+y^2x+xy+xy
=....确定题目没抄错吗？应该后面还有项漏抄了。。如果没错，这样就是最简式了
(4)原式=x^4-x^3+x^3-x^2+x^2-x-3x+6
=(x^4-x^3)+(x^3-x^2)+(x^2-x)-(3x-6)=(x-1)(x^3+x^2+x-3)
=(x-1)[(x^3-1)+(x^2-1)+(x-1)]
=(x-1)^2(x^2+2x+3)
(5)原式=m^4+64n^4+16m^2n^2-16m^2n^2
=(m^2+8n^2)^2-(4mn)^2
=(m^2+8n^2+4mn)(m^2+8n^2-4mn)
分解因式的思路一般都是能配方的就配方，提取公因式！

收起

1.=(a+1)(b+1)(c+1)先提出其中一项
2.=（x+1）(x-2）（x+3)先把2x^2分成x^2+x^2再提出（x+1）
3.你好像没写全
4.=x^4-x^3+x^3-x^2+x^2-4x+3
=(x-1）（x^3+x^2+x-3）
5.有点问题